We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric...We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric and the nonparametric components proposed. In the final of this paper, as a result, we got the variance decomposition of the model and establish the asymptotic convergence rate for estimator.展开更多
In this paper, we propose the double-penalized quantile regression estimators in partially linear models. An iterative algorithm is proposed for solving the proposed optimization problem. Some numerical examples illus...In this paper, we propose the double-penalized quantile regression estimators in partially linear models. An iterative algorithm is proposed for solving the proposed optimization problem. Some numerical examples illustrate that the finite sample performances of proposed method perform better than the least squares based method with regard to the non-causal selection rate (NSR) and the median of model error (MME) when the error distribution is heavy-tail. Finally, we apply the proposed methodology to analyze the ragweed pollen level dataset.展开更多
Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Mulle...Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.展开更多
This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） prop...This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.展开更多
In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard n...In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environmen...The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environment.This study aims to build a prediction model to understand the spatial characteristics and piecewise effects of forest fire drivers.Using monthly grid data from 2006 to 2020,a modeling study analyzed fire occurrences during the September to April fire season in Fujian Province,China.We compared the fitting performance of the logistic regression model(LRM),the generalized additive logistic model(GALM),and the spatial generalized additive logistic model(SGALM).The results indicate that SGALMs had the best fitting results and the highest prediction accuracy.Meteorological factors significantly impacted forest fires in Fujian Province.Areas with high fire incidence were mainly concentrated in the northwest and southeast.SGALMs improved the fitting effect of fire prediction models by considering spatial effects and the flexible fitting ability of nonlinear interpretation.This model provides piecewise interpretations of forest wildfire occurrences,which can be valuable for relevant departments and will assist forest managers in refining prevention measures based on temporal and spatial differences.展开更多
In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a...In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.展开更多
Traumatic brain injury(TBI) at a young age can lead to the development of long-term functional impairments. Severity of injury is well demonstrated to have a strong influence on the extent of functional impairments;ho...Traumatic brain injury(TBI) at a young age can lead to the development of long-term functional impairments. Severity of injury is well demonstrated to have a strong influence on the extent of functional impairments;however, identification of specific magnetic resonance imaging(MRI) biomarkers that are most reflective of injury severity and functional prognosis remain elusive. Therefore, the objective of this study was to utilize advanced statistical approaches to identify clinically relevant MRI biomarkers and predict functional outcomes using MRI metrics in a translational large animal piglet TBI model. TBI was induced via controlled cortical impact and multiparametric MRI was performed at 24 hours and 12 weeks post-TBI using T1-weighted, T2-weighted, T2-weighted fluid attenuated inversion recovery, diffusion-weighted imaging, and diffusion tensor imaging. Changes in spatiotemporal gait parameters were also assessed using an automated gait mat at 24 hours and 12 weeks post-TBI. Principal component analysis was performed to determine the MRI metrics and spatiotemporal gait parameters that explain the largest sources of variation within the datasets. We found that linear combinations of lesion size and midline shift acquired using T2-weighted imaging explained most of the variability of the data at both 24 hours and 12 weeks post-TBI. In addition, linear combinations of velocity, cadence, and stride length were found to explain most of the gait data variability at 24 hours and 12 weeks post-TBI. Linear regression analysis was performed to determine if MRI metrics are predictive of changes in gait. We found that both lesion size and midline shift are significantly correlated with decreases in stride and step length. These results from this study provide an important first step at identifying relevant MRI and functional biomarkers that are predictive of functional outcomes in a clinically relevant piglet TBI model. This study was approved by the University of Georgia Institutional Animal Care and Use Committee(AUP: A2015 11-001) on December 22, 2015.展开更多
High-dimensional heterogeneous data have acquired increasing attention and discussion in the past decade.In the context of heterogeneity,semiparametric regression emerges as a popular method to model this type of data...High-dimensional heterogeneous data have acquired increasing attention and discussion in the past decade.In the context of heterogeneity,semiparametric regression emerges as a popular method to model this type of data in statistics.In this paper,we leverage the benefits of expectile regression for computational efficiency and analytical robustness in heterogeneity,and propose a regularized partially linear additive expectile regression model with a nonconvex penalty,such as SCAD or MCP,for high-dimensional heterogeneous data.We focus on a more realistic scenario where the regression error exhibits a heavy-tailed distribution with only finite moments.This scenario challenges the classical sub-gaussian distribution assumption and is more prevalent in practical applications.Under certain regular conditions,we demonstrate that with probability tending to one,the oracle estimator is one of the local minima of the induced optimization problem.Our theoretical analysis suggests that the dimensionality of linear covariates that our estimation procedure can handle is fundamentally limited by the moment condition of the regression error.Computationally,given the nonconvex and nonsmooth nature of the induced optimization problem,we have developed a two-step algorithm.Finally,our method’s effectiveness is demonstrated through its high estimation accuracy and effective model selection,as evidenced by Monte Carlo simulation studies and a real-data application.Furthermore,by taking various expectile weights,our method effectively detects heterogeneity and explores the complete conditional distribution of the response variable,underscoring its utility in analyzing high-dimensional heterogeneous data.展开更多
This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression,which combines the common linear model with the functional linear regression model.The outstandi...This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression,which combines the common linear model with the functional linear regression model.The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases.The slope function is fitted by B-spline.Under suitable conditions,the authors obtain the convergence rates and asymptotic normality of the estimators.Finally,simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method.Both the simulation results and the real data analysis confirm that the newly proposed method works very well.展开更多
We consider the semiparametric partially linear regression models with mean function XTβ ＋ g（z）, where X and z are functional data. The new estimators of β and g（z） are presented and some asymptotic results are...We consider the semiparametric partially linear regression models with mean function XTβ ＋ g（z）, where X and z are functional data. The new estimators of β and g（z） are presented and some asymptotic results are given. The strong convergence rates of the proposed estimators are obtained. In our estimation, the observation number of each subject will be completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.展开更多
As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correla...As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.展开更多
This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables....This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.展开更多
This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown ...This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.展开更多
Consider a partially linear regression model with an unknown vector parameter , an unknown function g(·), and unknown heteroscedastic error variances. Chen, You<SUP>[23]</SUP> proposed a semiparametri...Consider a partially linear regression model with an unknown vector parameter , an unknown function g(·), and unknown heteroscedastic error variances. Chen, You<SUP>[23]</SUP> proposed a semiparametric generalized least squares estimator (SGLSE) for , which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].展开更多
In this paper,we focus on the partially linear varying-coefficient quantile regression with missing observations under ultra-high dimension,where the missing observations include either responses or covariates or the ...In this paper,we focus on the partially linear varying-coefficient quantile regression with missing observations under ultra-high dimension,where the missing observations include either responses or covariates or the responses and part of the covariates are missing at random,and the ultra-high dimension implies that the dimension of parameter is much larger than sample size.Based on the B-spline method for the varying coefficient functions,we study the consistency of the oracle estimator which is obtained only using active covariates whose coefficients are nonzero.At the same time,we discuss the asymptotic normality of the oracle estimator for the linear parameter.Note that the active covariates are unknown in practice,non-convex penalized estimator is investigated for simultaneous variable selection and estimation,whose oracle property is also established.Finite sample behavior of the proposed methods is investigated via simulations and real data analysis.展开更多
文摘We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric and the nonparametric components proposed. In the final of this paper, as a result, we got the variance decomposition of the model and establish the asymptotic convergence rate for estimator.
文摘In this paper, we propose the double-penalized quantile regression estimators in partially linear models. An iterative algorithm is proposed for solving the proposed optimization problem. Some numerical examples illustrate that the finite sample performances of proposed method perform better than the least squares based method with regard to the non-causal selection rate (NSR) and the median of model error (MME) when the error distribution is heavy-tail. Finally, we apply the proposed methodology to analyze the ragweed pollen level dataset.
文摘Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.
基金supported by the National Natural Science Funds for Distinguished Young Scholar (70825004)National Natural Science Foundation of China (NSFC) (10731010 and 10628104)+3 种基金the National Basic Research Program (2007CB814902)Creative Research Groups of China (10721101)Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics211 Project for Shanghai University of Financeand Economics (the 3rd phase)
文摘This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.
文摘In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
基金supported by the Fujian Provincial Science and Technology Program“University-Industry Cooperation Project”(2024Y4015)National Key R&D Plan of Strategic International Scientific and Technological Innovation Cooperation Project(2018YFE0207800).
文摘The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environment.This study aims to build a prediction model to understand the spatial characteristics and piecewise effects of forest fire drivers.Using monthly grid data from 2006 to 2020,a modeling study analyzed fire occurrences during the September to April fire season in Fujian Province,China.We compared the fitting performance of the logistic regression model(LRM),the generalized additive logistic model(GALM),and the spatial generalized additive logistic model(SGALM).The results indicate that SGALMs had the best fitting results and the highest prediction accuracy.Meteorological factors significantly impacted forest fires in Fujian Province.Areas with high fire incidence were mainly concentrated in the northwest and southeast.SGALMs improved the fitting effect of fire prediction models by considering spatial effects and the flexible fitting ability of nonlinear interpretation.This model provides piecewise interpretations of forest wildfire occurrences,which can be valuable for relevant departments and will assist forest managers in refining prevention measures based on temporal and spatial differences.
文摘In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.
基金Financial support was provided by the University of Georgia Office of the Vice President for Research to FDW。
文摘Traumatic brain injury(TBI) at a young age can lead to the development of long-term functional impairments. Severity of injury is well demonstrated to have a strong influence on the extent of functional impairments;however, identification of specific magnetic resonance imaging(MRI) biomarkers that are most reflective of injury severity and functional prognosis remain elusive. Therefore, the objective of this study was to utilize advanced statistical approaches to identify clinically relevant MRI biomarkers and predict functional outcomes using MRI metrics in a translational large animal piglet TBI model. TBI was induced via controlled cortical impact and multiparametric MRI was performed at 24 hours and 12 weeks post-TBI using T1-weighted, T2-weighted, T2-weighted fluid attenuated inversion recovery, diffusion-weighted imaging, and diffusion tensor imaging. Changes in spatiotemporal gait parameters were also assessed using an automated gait mat at 24 hours and 12 weeks post-TBI. Principal component analysis was performed to determine the MRI metrics and spatiotemporal gait parameters that explain the largest sources of variation within the datasets. We found that linear combinations of lesion size and midline shift acquired using T2-weighted imaging explained most of the variability of the data at both 24 hours and 12 weeks post-TBI. In addition, linear combinations of velocity, cadence, and stride length were found to explain most of the gait data variability at 24 hours and 12 weeks post-TBI. Linear regression analysis was performed to determine if MRI metrics are predictive of changes in gait. We found that both lesion size and midline shift are significantly correlated with decreases in stride and step length. These results from this study provide an important first step at identifying relevant MRI and functional biomarkers that are predictive of functional outcomes in a clinically relevant piglet TBI model. This study was approved by the University of Georgia Institutional Animal Care and Use Committee(AUP: A2015 11-001) on December 22, 2015.
基金Supported by the Hangzhou Joint Fund of the Zhejiang Provincial Natural Science Foundation of Chi-na(LHZY24A010002)the MOE Project of Humanities and Social Sciences(21YJCZH235).
文摘High-dimensional heterogeneous data have acquired increasing attention and discussion in the past decade.In the context of heterogeneity,semiparametric regression emerges as a popular method to model this type of data in statistics.In this paper,we leverage the benefits of expectile regression for computational efficiency and analytical robustness in heterogeneity,and propose a regularized partially linear additive expectile regression model with a nonconvex penalty,such as SCAD or MCP,for high-dimensional heterogeneous data.We focus on a more realistic scenario where the regression error exhibits a heavy-tailed distribution with only finite moments.This scenario challenges the classical sub-gaussian distribution assumption and is more prevalent in practical applications.Under certain regular conditions,we demonstrate that with probability tending to one,the oracle estimator is one of the local minima of the induced optimization problem.Our theoretical analysis suggests that the dimensionality of linear covariates that our estimation procedure can handle is fundamentally limited by the moment condition of the regression error.Computationally,given the nonconvex and nonsmooth nature of the induced optimization problem,we have developed a two-step algorithm.Finally,our method’s effectiveness is demonstrated through its high estimation accuracy and effective model selection,as evidenced by Monte Carlo simulation studies and a real-data application.Furthermore,by taking various expectile weights,our method effectively detects heterogeneity and explores the complete conditional distribution of the response variable,underscoring its utility in analyzing high-dimensional heterogeneous data.
基金supported by the National Natural Science Foundation of China under Grant Nos.11671096,11690013,11731011。
文摘This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression,which combines the common linear model with the functional linear regression model.The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases.The slope function is fitted by B-spline.Under suitable conditions,the authors obtain the convergence rates and asymptotic normality of the estimators.Finally,simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method.Both the simulation results and the real data analysis confirm that the newly proposed method works very well.
文摘We consider the semiparametric partially linear regression models with mean function XTβ ＋ g（z）, where X and z are functional data. The new estimators of β and g（z） are presented and some asymptotic results are given. The strong convergence rates of the proposed estimators are obtained. In our estimation, the observation number of each subject will be completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.
基金Chuanhua Wei’s research was supported by the National Natural Science Foundation of China(11301565)Jin Yang’s research was supported by the Post-doctoral Fellowship of Nankai University
文摘As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.
基金supported by National Natural Science Foundation of China(Grant No.11071120)
文摘This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.
基金supported by the Natural Science Foundation of China under Grant Nos.11231010,11471223,11501586BCMIIS and Key Project of Beijing Municipal Educational Commission under Grant No.KZ201410028030
文摘This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.
文摘Consider a partially linear regression model with an unknown vector parameter , an unknown function g(·), and unknown heteroscedastic error variances. Chen, You<SUP>[23]</SUP> proposed a semiparametric generalized least squares estimator (SGLSE) for , which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].
基金Supported by National Natural Science Foundation of China(Grant No.12071348)Fundamental Research Funds for Central Universities,China(Grant No.2023-3-2D-04)。
文摘In this paper,we focus on the partially linear varying-coefficient quantile regression with missing observations under ultra-high dimension,where the missing observations include either responses or covariates or the responses and part of the covariates are missing at random,and the ultra-high dimension implies that the dimension of parameter is much larger than sample size.Based on the B-spline method for the varying coefficient functions,we study the consistency of the oracle estimator which is obtained only using active covariates whose coefficients are nonzero.At the same time,we discuss the asymptotic normality of the oracle estimator for the linear parameter.Note that the active covariates are unknown in practice,non-convex penalized estimator is investigated for simultaneous variable selection and estimation,whose oracle property is also established.Finite sample behavior of the proposed methods is investigated via simulations and real data analysis.
