In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to t...In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to the mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented. A numerical example illustrates that the method is available.展开更多
A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic infe...A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvatures for multinomial nonlinear models. Our previous results [15] for ordinarynonlinear regression models are extended to multinomial nonlinear models.展开更多
This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivale...This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.展开更多
Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） ...Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.展开更多
A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvat...A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.展开更多
Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. How...Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.展开更多
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood e...In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.展开更多
This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power ...This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.展开更多
It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponent...It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.展开更多
In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properti...In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.展开更多
In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. O...In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).展开更多
This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） w...This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.展开更多
This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models ...This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].展开更多
Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobs...Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding.The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored.In this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models.The proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome variables.The proposed estimator is consistent and asymptotically normally distributed.Simulation studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error terms.Finally,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.展开更多
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model an...Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.展开更多
In this article,a partially nonlinear model with random effects is proposed and its new estimation procession is provided.In order to estimate the link function,we propose generalised leastsquare estimate and B-spline...In this article,a partially nonlinear model with random effects is proposed and its new estimation procession is provided.In order to estimate the link function,we propose generalised leastsquare estimate and B-splines estimate methods.Further,we also use the Gauss–Newton methodto construct the estimates of unknown parameters.Finally,we also consider the estimation forthe variance components.The consistency and the asymptotic normality of the estimator will beproved.Simulated and real examples are given to illustrate our proposed methodology,whichshows that our methods give effective estimation.展开更多
Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemen...Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.展开更多
A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kin...A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.展开更多
Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the ...Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the （Sx, Sv） plane. We give the condition for the occurrence of IGHZ}sy, in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.展开更多
The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR（1） errors. The elliptical class includes several symmetric multivar...The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR（1） errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-S, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-squave and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.展开更多
基金The research project supported by NSFC(1 9631 0 4 0 ) and NSFJ
文摘In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to the mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented. A numerical example illustrates that the method is available.
文摘A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvatures for multinomial nonlinear models. Our previous results [15] for ordinarynonlinear regression models are extended to multinomial nonlinear models.
文摘This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.
基金Supported by the National Natural Sciences Foundation of China (10761011)Mathematical Tianyuan Fund of National Natural Science Fundation of China(10626048)
文摘Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.
基金The project supported by NSFC!(19631040)NSFJ!(BK99002)
文摘A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.
基金supported in part by the National Nature Science Foundation of China(Nos.62173091,62073082)in part by the Natural Science Foundation of Fujian Province(No.2023J01268)in part by the Taishan Scholar Program of Shandong Province.
文摘Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.
基金The National Natural Science Foundation of China(No.11171065)the Natural Science Foundation of Jiangsu Province(No.BK2011058)
文摘In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.
基金Supported by SSFC（04BTJ002）,the National Natural Science Foundation of China（10371016） and the Post-Doctorial Grant in Southeast University.
文摘This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.
基金Supported by the National Natural Science Foundations of China( 1 9631 0 4 0 ) and SSFC( o2 BTJ0 0 1 ) .
文摘It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.
基金supported by the National Natural Science Foundation of China(No.12571284,No.12171203)supported by the National Natural Science Foundation of China(No.12561051)+3 种基金the Fundamental Research Funds for the Central Universities(No.23JNQMX21)supported by the University-level scientific research project of Guangdong University of Foreign Studies(NO.299-GK25G301/25TS10)supported by a grant from National Natural Foundation of China(No.12171225)Yunnan Province Xing Dian Talent Support Program(YNWR-YLXZ-2018-020)。
文摘In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.
基金The project supported by NNSFC (19631040), NSSFC (04BTJ002) and the grant for post-doctor fellows in SELF.
文摘In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).
基金Supported by National Natural Science Foundation of China (No. 10761011,10671139,10901135)Natural Science Foundation of Yunnan Province(No. 2008CD081)Special Foundation for Middle and Young Excellent Teachers of Yunnan University
文摘This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.
基金the Natural Science Foundation of Yunnan University （No. 2005Z007C） the Scientific Research Fund of Yunnan Provincial Education Department （No. 5Y0062A）+1 种基金 Mathematical Tianyuan Fund of National Natural Science Foundation of China （No. 10626048） Special Foundation for Middle and Young Excellent Teachers of Yunnan University.
文摘This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].
基金supported by the National Natural Science Foundation of China (Nos.12101545)by the natural science foundation of Inner Mongolia Autonomous Region (2022MS01007)。
文摘Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding.The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored.In this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models.The proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome variables.The proposed estimator is consistent and asymptotically normally distributed.Simulation studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error terms.Finally,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.
基金supported by National Natural Science Foundation of China (Grant Nos. 10561008, 10761011)Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. Y200805073)+1 种基金PhD Special Scientific Research Foundation of Chinese University (Grant No. 20060673002)Program for New Century Excellent Talents in University (Grant No. NCET-07-0737)
文摘Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
基金This research was supported by the National Natural Science Foundation of China[grant number 11471160],[grant number 11101114],[grant number 11571112]the National Statistical Science Research Key Program of China[grant number 2013LZ45]+1 种基金the Fundamental Research Funds for the Central Universities[grant number 30920130111015]the Jiangsu Provincial Basic Research Program(Natural Science Foundation)[grant number BK20131345]and sponsored by Qing Lan Project.
文摘In this article,a partially nonlinear model with random effects is proposed and its new estimation procession is provided.In order to estimate the link function,we propose generalised leastsquare estimate and B-splines estimate methods.Further,we also use the Gauss–Newton methodto construct the estimates of unknown parameters.Finally,we also consider the estimation forthe variance components.The consistency and the asymptotic normality of the estimator will beproved.Simulated and real examples are given to illustrate our proposed methodology,whichshows that our methods give effective estimation.
基金Project supported by the College Young Talents Foundation of Anhui Province,China (Grant No.2010SQRL107)
文摘Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.
文摘A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.
基金Project supported by the College Young Talents Foundation of Anhui Province,China(Grant No.2010SQRL107)the Natural Science Foundation of the Education Department of Anhui Province,China(Grant No.KJ2008B83ZC)the Natural Science Foundation of Anhui Province,China(Grant No.KJ2011Z234)
文摘Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the （Sx, Sv） plane. We give the condition for the occurrence of IGHZ}sy, in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.
基金Supported by the National Natural Science Foundation of China (No. 11171065 and NSFJSBK2011058)
文摘The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR（1） errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-S, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-squave and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.
