A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes.Moreover,data that arise from a heterogeneous population can be...A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes.Moreover,data that arise from a heterogeneous population can be efficiently analysed by a finite mixture of regression models.These observations motivate us to propose a novel finite mixture of median regression model based on a mixture of the skew-normal distributions to explore asymmetrical data from several subpopulations.With the appropriate choice of the tuning parameters,we establish the theoretical properties of the proposed procedure,including consistency for variable selection method and the oracle property in estimation.A productive nonparametric clustering method is applied to select the number of components,and an efficient EM algorithm for numerical computations is developed.Simulation studies and a real data set are used to illustrate the performance of the proposed methodologies.展开更多
In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their uppe...In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their upper bounds are given. For the problem of estimating the median,some optimum estimating functions based on the information matrices are acquired. Undersome regularity conditions, an approach to carrying out the best basis function is introduced. Innonlinear regression models, an optimum estimating function based on the information matricesis obtained. Some examples are given to illustrate the results. Finally, the concept of optimumestimating function and the methods of constructing optimum estimating function are developedin more general statistical models.展开更多
This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation an...This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation and in the meantime, preserves the same asymptotic normal distribution for the estimator, as in the ordinary minimum L_1-norm estimates.展开更多
当数据呈现厚尾特征或含有异常值时,基于惩罚最小二乘或似然函数的传统变量选择方法往往表现不佳.本文基于中位数回归和贝叶斯推断方法,研究线性模型的贝叶斯变量选择问题.通过选取回归系数的Spike and Slab先验,利用贝叶斯模型选择理...当数据呈现厚尾特征或含有异常值时,基于惩罚最小二乘或似然函数的传统变量选择方法往往表现不佳.本文基于中位数回归和贝叶斯推断方法,研究线性模型的贝叶斯变量选择问题.通过选取回归系数的Spike and Slab先验,利用贝叶斯模型选择理论提出了中位数回归的贝叶斯估计方法,并提出了有效的后验Gibbs抽样程序.大量数值模拟和波士顿房价数据分析充分说明了所提方法的有效性.展开更多
基金the National Natural Science Foundation of China[grant number 11861041]the Natural Science Research Foundation of Kunming University of Science and Technology[grant number KKSY201907003].
文摘A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes.Moreover,data that arise from a heterogeneous population can be efficiently analysed by a finite mixture of regression models.These observations motivate us to propose a novel finite mixture of median regression model based on a mixture of the skew-normal distributions to explore asymmetrical data from several subpopulations.With the appropriate choice of the tuning parameters,we establish the theoretical properties of the proposed procedure,including consistency for variable selection method and the oracle property in estimation.A productive nonparametric clustering method is applied to select the number of components,and an efficient EM algorithm for numerical computations is developed.Simulation studies and a real data set are used to illustrate the performance of the proposed methodologies.
基金Project supported by the National Natural Science Foundation of China(No.10171051)and the Youth Teacher Foundation of Nankai University.
文摘In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their upper bounds are given. For the problem of estimating the median,some optimum estimating functions based on the information matrices are acquired. Undersome regularity conditions, an approach to carrying out the best basis function is introduced. Innonlinear regression models, an optimum estimating function based on the information matricesis obtained. Some examples are given to illustrate the results. Finally, the concept of optimumestimating function and the methods of constructing optimum estimating function are developedin more general statistical models.
基金Research supported By AFOSC, USA, under Contract F49620-85-0008oy NNSFC of China.
文摘This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation and in the meantime, preserves the same asymptotic normal distribution for the estimator, as in the ordinary minimum L_1-norm estimates.
文摘当数据呈现厚尾特征或含有异常值时,基于惩罚最小二乘或似然函数的传统变量选择方法往往表现不佳.本文基于中位数回归和贝叶斯推断方法,研究线性模型的贝叶斯变量选择问题.通过选取回归系数的Spike and Slab先验,利用贝叶斯模型选择理论提出了中位数回归的贝叶斯估计方法,并提出了有效的后验Gibbs抽样程序.大量数值模拟和波士顿房价数据分析充分说明了所提方法的有效性.
