In target tracking applications,the Doppler measurement contains information of the target range rate,which has the potential capability to improve the tracking performance.However,the nonlinear degree between the mea...In target tracking applications,the Doppler measurement contains information of the target range rate,which has the potential capability to improve the tracking performance.However,the nonlinear degree between the measurement and the target state increases with the introduction of the Doppler measurement.Therefore,target tracking in the Doppler radar is a nonlinear filtering problem.In order to handle this problem,the Kalman filter form of best linear unbiased estimation(BLUE)with position measurements is proposed,which is combined with the sequential filtering algorithm to handle the Doppler measurement further,where the statistic characteristic of the converted measurement error is calculated based on the predicted information in the sequential filter.Moreover,the algorithm is extended to the maneuvering target tracking case,where the interacting multiple model(IMM)algorithm is used as the basic framework and the model probabilities are updated according to the BLUE position filter and the sequential filter,and the final estimation is a weighted sum of the outputs from the sequential filters and the model probabilities.Simulation results show that compared with existing approaches,the proposed algorithm can realize target tracking with preferable tracking precision and the extended method can achieve effective maneuvering target tracking.展开更多
In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias es...In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.展开更多
In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(...In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.展开更多
Concrete in reinforced concrete structure (RC) is generally under significant compressive stress load. To guarantee required quality and ductility, various tests have to be conducted to measure the concrete’s compres...Concrete in reinforced concrete structure (RC) is generally under significant compressive stress load. To guarantee required quality and ductility, various tests have to be conducted to measure the concrete’s compressive strength based on ACI (American Concrete Institute) code. Investigations of recent devastating collapses of structures around the world showed that some of the collapses directly resulted from the poor quality of the concrete. The lesson learned from these tragedies is that guaranteeing high quality of concrete is one of the most important factors ensuring the safety of the reinforced concrete structure. In order to ensure high quality of concrete, a new method for analyzing and evaluating the concrete production process is called for. In this paper, the indices of fit and stable degree are proposed as basis to evaluate the fitness and stability of concrete’s compressive strength. These two indices are combined to define and evaluate the quality index of the compressive strength of concrete. Prin-ciples of statistics are used to derive the best estimators of these indices. Based on the outcome of the study, a concrete compres-sive strength quality control chart is proposed as a tool to help the evaluation process. Finally, a new evaluation procedure to assess the quality control capability of the individual concrete manufacturer is also proposed.展开更多
In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries mor...In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.展开更多
Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed...Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.展开更多
Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance make...Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance makes these traits complex to breed on account of several alleles contributing to the complete trait expression.We employed genome-wide association study in an association panel of 88 rice genotypes using 142 new candidate gene based SSR(cgSSR)markers,derived from yield-related candidate genes,with the efficient mixed-model association coupled mixed linear model for dissecting complete genetic control of grain size traits.A total of 10 significant associations were identified for four grain size-related characters(grain weight,grain length,grain width,and length-width ratio).Among the identified associations,seven marker trait associations explain more than 10%of the phenotypic variation,indicating major putative QTLs for respective traits.The allelic variations at genes OsBC1L4,SHO1 and OsD2 showed association between 1000-grain weight and grain width,1000-grain weight and grain length,and grain width and length-width ratio,respectively.The cgSSR markers,associated with corresponding traits,can be utilized for direct allelic selection,while other significantly associated cgSSRs may be utilized for allelic accumulation in the breeding programs or grain size improvement.The new cgSSR markers associated with grain size related characters have a significant impact on practical plant breeding to increase the number of causative alleles for these traits through marker aided rice breeding programs.展开更多
It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this...It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.展开更多
Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class c...Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.展开更多
The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application sc...The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application scenarios,which exhibits higher reliability by a weighted fusion of integer candidates.However,traditional BIE estimation with Gaussian distribution(GBIE)faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning,mainly due to the presence of outliers and unmodeled errors.To this end,an improved BIE estimation method with Laplacian distribution(LBIE)is proposed,and several key issues are discussed,including the weight function of LBIE,determination of the candidates included based on the OIA test,and derivation of the variance of LBIE solutions for reliability evaluation.The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution(TBIE),and significantly outperforms the ILS-PAR and GBIE methods.In an urban expressway test with a Huawei Mate40 smartphone,the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50%improvements compared to the ILS-PAR and GBIE methods.In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics,the positioning accuracy of LBIE in three directions is 0.112 m,0.107 m,and 0.252 m,respectively,with improvements of 17.6%,27.2%,and 26.1%compared to GBIE,and 23.3%,28.2%,and 30.6%compared to ILS-PAR.Moreover,its computational time increases by 30–40%compared to ILS-PAR and is approximately half of that using TBIE.展开更多
In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown u...In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.展开更多
Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown pos...Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X 1 : X 2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M 2 X 1β1under the model and its best linear unbiased estimators under the reduced linear models of are given, where M 2 = I -X 2 X 2 + . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M 2 X 1β1 under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model.展开更多
Linear mixed models are popularly used to fit continuous longitudinal data,and the random effects are commonly assumed to have normal distribution.However,this assumption needs to be tested so that further analysis ca...Linear mixed models are popularly used to fit continuous longitudinal data,and the random effects are commonly assumed to have normal distribution.However,this assumption needs to be tested so that further analysis can be proceeded well.In this paper,we consider the Baringhaus-Henze-Epps-Pulley(BHEP)tests,which are based on an empirical characteristic function.Differing from their case,we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors.The test is consistent against global alternatives,and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~where n is sample size.^-hlrthermore,to overcome the problem that the limiting null distribution of the test is not tractable,we suggest a new method:use a conditional Monte Carlo test(CMCT)to approximate the null distribution,and then to simulate p-values.The test is compared with existing methods,the power is examined,and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.展开更多
Industrial lignin waste is an important byproduct of bio-refineries and the paper industry.Depolymerization of industrial lignin could generate useful aromatic compounds.This group has focused on electrolytic decompos...Industrial lignin waste is an important byproduct of bio-refineries and the paper industry.Depolymerization of industrial lignin could generate useful aromatic compounds.This group has focused on electrolytic decomposition of biorefinery lignin.To quantify electrolytic decomposition of the lignin in a highly caustic solution,ultraviolet(UV)spectroscopy provides a useful probe.The conversion of the neat lignin to the oxidized products achieved by the electrolytic reactor may be measured by quantifying the amount of unreacted neat lignin that remains in the effluent.Because the properties of electrolytic decomposition products are largely unknown,a useful approach to quantify decomposition of the neat lignin is to use a multivariate calibration method referred to as the generalized standard addition method(GSAM).In this approach,the electrolytic decomposition products represent a background interference and the neat lignin that remains can be quantified.This approach allows the conversion of the neat lignin to be calculated in a solution that is a complex mixture.展开更多
In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. T...In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. The stresses, applied repeatedly at random cycle times, will causethe degradation of strength. In addition, the number of cycles in an interval is assumed to followa Poisson distribution. In the case of the strength and stress random variables following exponential distributions, the expression for the reliability of the proposed dynamic stress–strengthmodel is derived based on survival signature. The reliability is estimated by using the best linearunbiased estimation (BLUE). Considering the Type-II censored failure times, the best linear unbiased predictors (BLUP) for the unobserved coherent system failure times are developed basedon the observed failure times. Monte Carlo simulations are performed to compare the BLUE ofparameters with different values and compute the BLUP. A real data set is also analysed for anillustration of the findings.展开更多
Among all the ambiguity resolution techniques,the Full Ambiguity Resolution(FAR),Partial Ambiguity Resolution(PAR)and Best Integer Equivariant(BIE)estimator are widely used.Although the researches have been done on th...Among all the ambiguity resolution techniques,the Full Ambiguity Resolution(FAR),Partial Ambiguity Resolution(PAR)and Best Integer Equivariant(BIE)estimator are widely used.Although the researches have been done on the different classes of ambiguity resolution,we still hope to find the relationships among these specific algorithms.In this work,we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates.A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived.Then,we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution(MICAR)to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR(FAR)algorithm instead of BIE.In the experiments,we utilize the simulated data of GPS(Global Positioning System)+BDS(BeiDou Navigation Satellite System)+Galileo(Galileo navigation satellite system)to contrast the effects of MICAR and single candidate estimator,i.e.,FAR.By taking the threshold of 5 cm at 95%confidence level as an example,MICAR accelerates the convergence process by about 3.0 min.When the positioning sequence converges,MICAR reduces the root mean square of the positioning error by 9.8%in horizontal directions and 3.5%in vertical direction,which is attributed to more fixed NL.展开更多
Let X_1,...,Xn. be a random sample from multivariate normal distribution Np(μ,∑), where μ∈Rp and E is a positive definite matrix, both p and ∑ being unknown. It is shown that for the entropy loss L(δ, |∑| ^(- 1...Let X_1,...,Xn. be a random sample from multivariate normal distribution Np(μ,∑), where μ∈Rp and E is a positive definite matrix, both p and ∑ being unknown. It is shown that for the entropy loss L(δ, |∑| ^(- 1) )=δ/ |∑| ^(- 1) -log(δ/ |∑ |~ (- 1) ) - 1 , the best affine equivariant estimator of the generalized precision |∑|^(-1) is inadmissible and three classes of improved estimators are given.展开更多
Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and co...Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and computational formula which can assess the disturbing influence.展开更多
基金This work was supported by the Basic Research Operation Foundation for Central University(ZYGX2016J039).
文摘In target tracking applications,the Doppler measurement contains information of the target range rate,which has the potential capability to improve the tracking performance.However,the nonlinear degree between the measurement and the target state increases with the introduction of the Doppler measurement.Therefore,target tracking in the Doppler radar is a nonlinear filtering problem.In order to handle this problem,the Kalman filter form of best linear unbiased estimation(BLUE)with position measurements is proposed,which is combined with the sequential filtering algorithm to handle the Doppler measurement further,where the statistic characteristic of the converted measurement error is calculated based on the predicted information in the sequential filter.Moreover,the algorithm is extended to the maneuvering target tracking case,where the interacting multiple model(IMM)algorithm is used as the basic framework and the model probabilities are updated according to the BLUE position filter and the sequential filter,and the final estimation is a weighted sum of the outputs from the sequential filters and the model probabilities.Simulation results show that compared with existing approaches,the proposed algorithm can realize target tracking with preferable tracking precision and the extended method can achieve effective maneuvering target tracking.
文摘In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.
基金the National Natural Science Foundation of China(11901236)Scienti c Research Fund of Hunan Provincial Science and Technology Department(2019JJ50479)+1 种基金Scienti c Research Fund of Hunan Provincial Education Department(18B322)Fundamental Research Fund of Xiangxi Autonomous Prefec-ture(2018SF5026).
文摘In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.
基金Project (No. NSC92-2213-e-167-001) supported by the National Science Council, Taiwan, China
文摘Concrete in reinforced concrete structure (RC) is generally under significant compressive stress load. To guarantee required quality and ductility, various tests have to be conducted to measure the concrete’s compressive strength based on ACI (American Concrete Institute) code. Investigations of recent devastating collapses of structures around the world showed that some of the collapses directly resulted from the poor quality of the concrete. The lesson learned from these tragedies is that guaranteeing high quality of concrete is one of the most important factors ensuring the safety of the reinforced concrete structure. In order to ensure high quality of concrete, a new method for analyzing and evaluating the concrete production process is called for. In this paper, the indices of fit and stable degree are proposed as basis to evaluate the fitness and stability of concrete’s compressive strength. These two indices are combined to define and evaluate the quality index of the compressive strength of concrete. Prin-ciples of statistics are used to derive the best estimators of these indices. Based on the outcome of the study, a concrete compres-sive strength quality control chart is proposed as a tool to help the evaluation process. Finally, a new evaluation procedure to assess the quality control capability of the individual concrete manufacturer is also proposed.
基金Supported by National Science Foundation of China(11901236,12261036),Scientific Research Fund of Hunan Provincial Education Department(21A0328)Provincial Natural Science Foundation of Hunan(2022JJ30469)+1 种基金Young Core Teacher Foundation of Hunan Province([2020]43)Jishou University Laboratory Program(JDDL2017001,JDLF2021024).
文摘In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.
基金Supported by the National Natural Science Foundation of China(11901236)the Scientific Research Fund of Hunan Provincial Science and Technology Department(2019JJ50479)+3 种基金the Scientific Research Fund of Hunan Provincial Education Department(18B322)the Winning Bid Project of Hunan Province for the 4th National Economic Census([2020]1)the Young Core Teacher Foundation of Hunan Province([2020]43)the Funda-mental Research Fund of Xiangxi Autonomous Prefecture(2018SF5026)。
文摘Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.
基金ICAR-National Rice Research Institute for financial support
文摘Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance makes these traits complex to breed on account of several alleles contributing to the complete trait expression.We employed genome-wide association study in an association panel of 88 rice genotypes using 142 new candidate gene based SSR(cgSSR)markers,derived from yield-related candidate genes,with the efficient mixed-model association coupled mixed linear model for dissecting complete genetic control of grain size traits.A total of 10 significant associations were identified for four grain size-related characters(grain weight,grain length,grain width,and length-width ratio).Among the identified associations,seven marker trait associations explain more than 10%of the phenotypic variation,indicating major putative QTLs for respective traits.The allelic variations at genes OsBC1L4,SHO1 and OsD2 showed association between 1000-grain weight and grain width,1000-grain weight and grain length,and grain width and length-width ratio,respectively.The cgSSR markers,associated with corresponding traits,can be utilized for direct allelic selection,while other significantly associated cgSSRs may be utilized for allelic accumulation in the breeding programs or grain size improvement.The new cgSSR markers associated with grain size related characters have a significant impact on practical plant breeding to increase the number of causative alleles for these traits through marker aided rice breeding programs.
文摘It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.
文摘Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.
基金funded by the National Key R&D Program of China(Grant No.2021YFC3000502)the National Natural Science Foundation of China(Grant No.42274034)+2 种基金the Major Program(JD)of Hubei Province(Grant No.2023BAA026)the Special Fund of Hubei Luojia Laboratory(Grant No.2201000038)the Research project of Chongqing Administration for Marktet Regulation,China(Grant No.CQSJKJ2022037).
文摘The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application scenarios,which exhibits higher reliability by a weighted fusion of integer candidates.However,traditional BIE estimation with Gaussian distribution(GBIE)faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning,mainly due to the presence of outliers and unmodeled errors.To this end,an improved BIE estimation method with Laplacian distribution(LBIE)is proposed,and several key issues are discussed,including the weight function of LBIE,determination of the candidates included based on the OIA test,and derivation of the variance of LBIE solutions for reliability evaluation.The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution(TBIE),and significantly outperforms the ILS-PAR and GBIE methods.In an urban expressway test with a Huawei Mate40 smartphone,the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50%improvements compared to the ILS-PAR and GBIE methods.In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics,the positioning accuracy of LBIE in three directions is 0.112 m,0.107 m,and 0.252 m,respectively,with improvements of 17.6%,27.2%,and 26.1%compared to GBIE,and 23.3%,28.2%,and 30.6%compared to ILS-PAR.Moreover,its computational time increases by 30–40%compared to ILS-PAR and is approximately half of that using TBIE.
基金supported by National Science Foundation of China (Grant Nos.12261036 and 11901236)Scientific Research Fund of Hunan Provincial Education Department (Grant No.21A0328)+1 种基金Provincial Natural Science Foundation of Hunan (Grant No.2022JJ30469)Young Core Teacher Foundation of Hunan Province (Grant No.[2020]43)。
文摘In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.
基金supported by the National Natural Science Foundation of ChinaTian Yuan Special Foundation (No.10226024)Postdoctoral Foundation of China and Lab.of Math.for Nonlinear Sciences at Fudan Universitysupported in part by The International Organizing Committee and The Local Organizing Committee at the University of Tampere for this Workshopsupported in part by an NSF grant of China
文摘Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X 1 : X 2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M 2 X 1β1under the model and its best linear unbiased estimators under the reduced linear models of are given, where M 2 = I -X 2 X 2 + . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M 2 X 1β1 under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model.
基金supported in part by a grant of Research Grants Council of Hong Kong,and National Natural Science Foundation of China(Grant No.11101157)
文摘Linear mixed models are popularly used to fit continuous longitudinal data,and the random effects are commonly assumed to have normal distribution.However,this assumption needs to be tested so that further analysis can be proceeded well.In this paper,we consider the Baringhaus-Henze-Epps-Pulley(BHEP)tests,which are based on an empirical characteristic function.Differing from their case,we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors.The test is consistent against global alternatives,and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~where n is sample size.^-hlrthermore,to overcome the problem that the limiting null distribution of the test is not tractable,we suggest a new method:use a conditional Monte Carlo test(CMCT)to approximate the null distribution,and then to simulate p-values.The test is compared with existing methods,the power is examined,and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.
文摘Industrial lignin waste is an important byproduct of bio-refineries and the paper industry.Depolymerization of industrial lignin could generate useful aromatic compounds.This group has focused on electrolytic decomposition of biorefinery lignin.To quantify electrolytic decomposition of the lignin in a highly caustic solution,ultraviolet(UV)spectroscopy provides a useful probe.The conversion of the neat lignin to the oxidized products achieved by the electrolytic reactor may be measured by quantifying the amount of unreacted neat lignin that remains in the effluent.Because the properties of electrolytic decomposition products are largely unknown,a useful approach to quantify decomposition of the neat lignin is to use a multivariate calibration method referred to as the generalized standard addition method(GSAM).In this approach,the electrolytic decomposition products represent a background interference and the neat lignin that remains can be quantified.This approach allows the conversion of the neat lignin to be calculated in a solution that is a complex mixture.
基金This work is supported by the National Natural Science Foundation of China[71571144,71401134,71171164,11701406]The Natural Science Basic Research Program of Shaanxi Province[2015JM1003]The Program of international Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province[2016KW-033].
文摘In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. The stresses, applied repeatedly at random cycle times, will causethe degradation of strength. In addition, the number of cycles in an interval is assumed to followa Poisson distribution. In the case of the strength and stress random variables following exponential distributions, the expression for the reliability of the proposed dynamic stress–strengthmodel is derived based on survival signature. The reliability is estimated by using the best linearunbiased estimation (BLUE). Considering the Type-II censored failure times, the best linear unbiased predictors (BLUP) for the unobserved coherent system failure times are developed basedon the observed failure times. Monte Carlo simulations are performed to compare the BLUE ofparameters with different values and compute the BLUP. A real data set is also analysed for anillustration of the findings.
基金National Natural Science Foundation of China,42174029,Shengfeng Gu.
文摘Among all the ambiguity resolution techniques,the Full Ambiguity Resolution(FAR),Partial Ambiguity Resolution(PAR)and Best Integer Equivariant(BIE)estimator are widely used.Although the researches have been done on the different classes of ambiguity resolution,we still hope to find the relationships among these specific algorithms.In this work,we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates.A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived.Then,we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution(MICAR)to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR(FAR)algorithm instead of BIE.In the experiments,we utilize the simulated data of GPS(Global Positioning System)+BDS(BeiDou Navigation Satellite System)+Galileo(Galileo navigation satellite system)to contrast the effects of MICAR and single candidate estimator,i.e.,FAR.By taking the threshold of 5 cm at 95%confidence level as an example,MICAR accelerates the convergence process by about 3.0 min.When the positioning sequence converges,MICAR reduces the root mean square of the positioning error by 9.8%in horizontal directions and 3.5%in vertical direction,which is attributed to more fixed NL.
基金the National Natural Science Foundation of ChinaNow at Department of Mathematics, Huaiyin Teachers' College, Jiangsu, China
文摘Let X_1,...,Xn. be a random sample from multivariate normal distribution Np(μ,∑), where μ∈Rp and E is a positive definite matrix, both p and ∑ being unknown. It is shown that for the entropy loss L(δ, |∑| ^(- 1) )=δ/ |∑| ^(- 1) -log(δ/ |∑ |~ (- 1) ) - 1 , the best affine equivariant estimator of the generalized precision |∑|^(-1) is inadmissible and three classes of improved estimators are given.
文摘Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and computational formula which can assess the disturbing influence.
