In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance c...In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance components.However,there is still no related research in the mixed additive and multiplicative random error model(MAMREM).Based on the MAMREM,this paper applies the nonnegative least squares variance component estimation(NNLS-VCE)algorithm to this model.The correlation formula and iterative algorithm of NNLS-VCE for MAMREM are derived.The problem of negative variance in VCE for MAMREM is solved.This paper uses the digital simulation example and the Digital Terrain Mode(DTM)to prove the proposed algorithm's validity.The experimental results demonstrated that the proposed algorithm can effectively correct the VCE in MAMREM when there is a negative VCE.展开更多
The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-pr...The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.展开更多
A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inve...A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.展开更多
Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis...Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included. Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets. Results showed that MINQUE and REML methods performed equally regarding bias, Type I error, and power. Jackknife-based MINQUE and REML greatly improved power compared to non-Jackknife based linear mixed model approaches. Results also showed that MINQUE is more time-saving compared to REML, especially with the use of resampling techniques and large data set analysis. Results from the actual cotton data analysis were in agreement with our simulated results. Therefore, Jackknife-based MINQUE approaches could be recommended to achieve desirable power with reduced time for a large data analysis and model simulations.展开更多
The estimation of glacier flow velocity on a short-term scale is very important for further glacier dynamics research.In this study,10 Sentinel-1 ascending images and 10 Sentinel-1 descending images of Urumqi Glacier ...The estimation of glacier flow velocity on a short-term scale is very important for further glacier dynamics research.In this study,10 Sentinel-1 ascending images and 10 Sentinel-1 descending images of Urumqi Glacier No.1 in 2017 were used to calculate the glacier flow velocity in a high coherence period by DIn SAR technology and MAI technology,while the offset tracking technology was used to estimate the glacier flow velocity in a low coherence period.Then,the monthly three-dimensional flow velocity of the glacier was calculated by the Helmert variance component estimation method.Finally,the accuracy of the estimated glacier flow velocity on a monthly scale was evaluated.The results showed that:(1)the monthly scale motion velocity of Urumqi Glacier No.1 in May,June,July,and August 2017 was 0.273 m/month,0.657 m/month,0.582 m/month,and 0.392 m/month,respectively.(2)The accuracy of glacier surface velocity from May 2017 to August 2017 was 0.033 m/month,0.026 m/month,0.034 m/month and 0.037 m/month,respectively.(3)The accuracy of glacier surface flow velocity from May 2017 to August 2017 was 0.018 m/month,0.031 m/month,0.029 m/month and 0.030 m/month,respectively.Therefore,the research methodology based on the Sentinel-1 ascending and descending data and presented in this paper was applicable to the estimation of monthly-scale flow velocity of mountain glaciers.展开更多
Starting from the more general functional model and being based on their work of K. R. Koch (1986) and Ou Ziqiang (1989), marginal likelihood function of variance components is derived and is identical to the ortho...Starting from the more general functional model and being based on their work of K. R. Koch (1986) and Ou Ziqiang (1989), marginal likelihood function of variance components is derived and is identical to the orthogonal complement likelihood function in this paper. Minimum norm quadratic unibiased estimator (MINQUE) is developed, which expands the formula by C. R. Rao (1973). It is proved that Helmert type estimation, MINQUE, BQUE and maximum likelihood estimation are identical to one another. Besides, a universal formula for accuracy evalution is presented. Through these work, the paper establishes a universal theory of variance covariance components.展开更多
The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type est...The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type estimation (M-estimation) should replace LS estimation. The paper discusses robust estimations of parameter vector and variance components for corresponding error model based on the principle of maximum likelihood type estimations (M-estimations). The influence functions are given respectively.展开更多
基金supported by the National Natural Science Foundation of China(No.42174011)。
文摘In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance components.However,there is still no related research in the mixed additive and multiplicative random error model(MAMREM).Based on the MAMREM,this paper applies the nonnegative least squares variance component estimation(NNLS-VCE)algorithm to this model.The correlation formula and iterative algorithm of NNLS-VCE for MAMREM are derived.The problem of negative variance in VCE for MAMREM is solved.This paper uses the digital simulation example and the Digital Terrain Mode(DTM)to prove the proposed algorithm's validity.The experimental results demonstrated that the proposed algorithm can effectively correct the VCE in MAMREM when there is a negative VCE.
基金supported by the National Natural Science Foundation of China(No.41874001 and No.41664001)Support Program for Outstanding Youth Talents in Jiangxi Province(No.20162BCB23050)National Key Research and Development Program(No.2016YFB0501405)。
文摘The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.
文摘A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.
文摘Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included. Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets. Results showed that MINQUE and REML methods performed equally regarding bias, Type I error, and power. Jackknife-based MINQUE and REML greatly improved power compared to non-Jackknife based linear mixed model approaches. Results also showed that MINQUE is more time-saving compared to REML, especially with the use of resampling techniques and large data set analysis. Results from the actual cotton data analysis were in agreement with our simulated results. Therefore, Jackknife-based MINQUE approaches could be recommended to achieve desirable power with reduced time for a large data analysis and model simulations.
基金funded by the Basic scientific research fund projects(Youth Project)of the Educational Department of Liaoning Province in 2023(Grants No.JYTQN2023451)Liaoning Institute of Science and Technology doctoral research initiation fund project in 2023(Grants No.2307B27)+2 种基金Basic Research Project of Higher Education Institutions of Liaoning Provincial Department of Education(Grants No.2024JYTYB-12)the Basic scientific research fund projects(Youth Project)of the Educational Department of Liaoning Province in 2023(Grants No.JYTQN2024-21)Liaoning Institute of Science and Technology doctoral research initiation fund project in 2023(Grants No.2307B26)。
文摘The estimation of glacier flow velocity on a short-term scale is very important for further glacier dynamics research.In this study,10 Sentinel-1 ascending images and 10 Sentinel-1 descending images of Urumqi Glacier No.1 in 2017 were used to calculate the glacier flow velocity in a high coherence period by DIn SAR technology and MAI technology,while the offset tracking technology was used to estimate the glacier flow velocity in a low coherence period.Then,the monthly three-dimensional flow velocity of the glacier was calculated by the Helmert variance component estimation method.Finally,the accuracy of the estimated glacier flow velocity on a monthly scale was evaluated.The results showed that:(1)the monthly scale motion velocity of Urumqi Glacier No.1 in May,June,July,and August 2017 was 0.273 m/month,0.657 m/month,0.582 m/month,and 0.392 m/month,respectively.(2)The accuracy of glacier surface velocity from May 2017 to August 2017 was 0.033 m/month,0.026 m/month,0.034 m/month and 0.037 m/month,respectively.(3)The accuracy of glacier surface flow velocity from May 2017 to August 2017 was 0.018 m/month,0.031 m/month,0.029 m/month and 0.030 m/month,respectively.Therefore,the research methodology based on the Sentinel-1 ascending and descending data and presented in this paper was applicable to the estimation of monthly-scale flow velocity of mountain glaciers.
文摘Starting from the more general functional model and being based on their work of K. R. Koch (1986) and Ou Ziqiang (1989), marginal likelihood function of variance components is derived and is identical to the orthogonal complement likelihood function in this paper. Minimum norm quadratic unibiased estimator (MINQUE) is developed, which expands the formula by C. R. Rao (1973). It is proved that Helmert type estimation, MINQUE, BQUE and maximum likelihood estimation are identical to one another. Besides, a universal formula for accuracy evalution is presented. Through these work, the paper establishes a universal theory of variance covariance components.
文摘The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type estimation (M-estimation) should replace LS estimation. The paper discusses robust estimations of parameter vector and variance components for corresponding error model based on the principle of maximum likelihood type estimations (M-estimations). The influence functions are given respectively.
