Semiparametric variable selection for partially varying coefficient models with endogenous variables

By using instrumental variable technology and the partial group smoothly clipped absolute deviation penalty method, we propose a variable selection procedure for a class of partially varying coefficient models with endogenous variables. The proposed variable selection method can eliminate the influence of the endogenous variables. With appropriate selection of the tuning parameters, we establish the oracle property of this variable selection procedure. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

响应变量随机缺失下变系数模型的变量选择

In this paper,we present a variable selection procedure by combining basis function approximations with penalized estimating equations for varying-coefficient models with missing response at random.With appropriate selection of the tuning parameters,we establish the consistency of the variable selection procedure and the optimal convergence rate of the regularized estimators.A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

Variable selection for semiparametric varying-coefficient partially linear models with missing response at random

In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

半参数变系数部分线性模型的统计推断

本文在多种复杂数据下, 研究一类半参数变系数部分线性模型的统计推断理论和方法. 首先在纵向数据和测量误差数据等复杂数据下, 研究半参数变系数部分线性模型的经验似然推断问题, 分别提出分组的和纠偏的经验似然方法. 该方法可以有效地处理纵向数据的组内相关性给构造经验似然比函数所带来的困难. 其次在测量误差数据和缺失数据等复杂数据下, 研究模型的变量选择问题, 分别提出一个“纠偏” 的和基于借补值的变量选择方法. 该变量选择方法可以同时选择参数分量及非参数分量中的重要变量, 并且变量选择与回归系数的估计同时进行. 通过选择适当的惩罚参数, 证明该变量选择方法可以相合地识别出真实模型, 并且所得的正则估计具有oracle 性质.     

删失数据下变系数部分线性模型的经验似然变量选择

In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.     

Variable selection for generalized varying coefficient partially linear models with diverging number of parameters

Semiparametric models with diverging number of predictors arise in many contemporary scientific areas.Variable selection for these models consists of two components:model selection for non-parametric components and selection of significant variables for the parametric portion.In this paper,we consider a variable selection procedure by combining basis function approximation with SCAD penalty.The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components.With appropriate selection of tuning parameters,we establish the consistency and sparseness of this procedure.     

纵向数据下线性EV模型的变量选择

本文考虑了纵向数据线性EV模型的变量选择.基于二次推断函数方法和压缩方法的思想提出了一种新的偏差校正的变量选择方法.在选择适当的调整参数下,我们证明了所得到的估计量的相合性和渐近正态性.最后通过模拟研究验证了所提出的变量选择方法的有限样本性质.     

Model detection and variable selection for varying coefficient models with longitudinal data

In this paper, we consider the problem of variable selection and model detection in varying coefficient models with longitudinal data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.     

Variable Selection of Partially Linear Single-index Models

In this article, we study the variable selection of partially linear single-index model（PLSIM）. Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive ll penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.     

部分线性单指标模型的复合分位数回归及变量选择

本文提出复合最小化平均分位数损失估计方法 (composite minimizing average check loss estimation,CMACLE)用于实现部分线性单指标模型(partial linear single-index models,PLSIM)的复合分位数回归(composite quantile regression,CQR).首先基于高维核函数构造参数部分的复合分位数回归意义下的相合估计,在此相合估计的基础上,通过采用指标核函数进一步得到参数和非参数函数的可达最优收敛速度的估计,并建立所得估计的渐近正态性,比较PLSIM的CQR估计和最小平均方差估计(MAVE)的相对渐近效率.进一步地,本文提出CQR框架下PLSIM的变量选择方法,证明所提变量选择方法的oracle性质.随机模拟和实例分析验证了所提方法在有限样本时的表现,证实了所提方法的优良性.     

Variable Selection in General Frailty Models Using Penalized H-Likelihood

Variable selection methods using a penalized likelihood have been widely studied in various statistical models. However, in semiparametric frailty models, these methods have been relatively less studied because the marginal likelihood function involves analytically intractable integrals, particularly when modeling multicomponent or correlated frailties. In this article, we propose a simple but unified procedure via a penalized h-likelihood (HL) for variable selection of fixed effects in a general class of semiparametric frailty models, in which random effects may be shared, nested, or correlated. We consider three penalty functions (least absolute shrinkage and selection operator [LASSO], smoothly clipped absolute deviation [SCAD], and HL) in our variable selection procedure. We show that the proposed method can be easily implemented via a slight modification to existing HL estimation approaches. Simulation studies also show that the procedure using the SCAD or HL penalty performs well. The usefulness of the new method is illustrated using three practical datasets too. Supplementary materials for the article are available online.     

Variable selection in censored quantile regression with high dimensional data

We propose a two-step variable selection procedure for censored quantile regression with high dimensional predictors. To account for censoring data in high dimensional case, we employ effective dimension reduction and the ideas of informative subset idea. Under some regularity conditions, we show that our procedure enjoys the model selection consistency. Simulation study and real data analysis are conducted to evaluate the finite sample performance of the proposed approach.     

分位数变系数模型基于核光滑的变量选择

分位数变系数模型是一种稳健的非参数建模方法.使用变系数模型分析数据时,一个自然的问题是如何同时选择重要变量和从重要变量中识别常数效应变量.本文基于分位数方法研究具有稳健和有效性的估计和变量选择程序.利用局部光滑和自适应组变量选择方法,并对分位数损失函数施加双惩罚,我们获得了惩罚估计.通过BIC准则合适地选择调节参数,提出的变量选择方法具有oracle理论性质,并通过模拟研究和脂肪实例数据分析来说明新方法的有用性.数值结果表明,在不需要知道关于变量和误差分布的任何信息前提下,本文提出的方法能够识别不重要变量同时能区分出常数效应变量.     

Consistent tuning parameter selection in high dimensional sparse linear regression

An exhaustive search as required for traditional variable selection methods is impractical in high dimensional statistical modeling. Thus, to conduct variable selection, various forms of penalized estimators with good statistical and computational properties, have been proposed during the past two decades. The attractive properties of these shrinkage and selection estimators, however, depend critically on the size of regularization which controls model complexity. In this paper, we consider the problem of consistent tuning parameter selection in high dimensional sparse linear regression where the dimension of the predictor vector is larger than the size of the sample. First, we propose a family of high dimensional Bayesian Information Criteria (HBIC), and then investigate the selection consistency, extending the results of the extended Bayesian Information Criterion (EBIC), in Chen and Chen (2008) to ultra-high dimensional situations. Second, we develop a two-step procedure, the SIS+AENET, to conduct variable selection in p>n situations. The consistency of tuning parameter selection is established under fairly mild technical conditions. Simulation studies are presented to confirm theoretical findings, and an empirical example is given to illustrate the use in the internet advertising data.     

Variable selection for single-index varying-coefficient model

We consider the problem of variable selection for single-index varying-coefficient model, and present a regularized variable selection procedure by combining basis function approximations with SCAD penalty. The proposed procedure simultaneously selects significant covariates with functional coefficients and local significant variables with parametric coefficients. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. The proposed method can naturally be applied to deal with pure single-index model and varying-coefficient model. Finite sample performances of the proposed method are illustrated by a simulation study and the real data analysis.     

Model Selection for Variable Length Markov Chains and Tuning the Context Algorithm

We consider the model selection problem in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length. Various aims in selecting a VLMC can be formalized with different non-equivalent risks, such as final prediction error or expected Kullback-Leibler information. We consider the asymptotic behavior of different risk functions and show how they can be generally estimated with the same resampling strategy. Such estimated risks then yield new model selection criteria. In particular, we obtain a data-driven tuning of Rissanen's tree structured context algorithm which is a computationally feasible procedure for selection and estimation of a VLMC.     

Nonparametric variable selection and its application to additive models

Variable selection for multivariate nonparametric regression models usually involves parameterized approximation for nonparametric functions in the objective function. However, this parameterized approximation often increases the number of parameters significantly, leading to the “curse of dimensionality” and inaccurate estimation. In this paper, we propose a novel and easily implemented approach to do variable selection in nonparametric models without parameterized approximation, enabling selection consistency to be achieved. The proposed method is applied to do variable selection for additive models. A two-stage procedure with selection and adaptive estimation is proposed, and the properties of this method are investigated. This two-stage algorithm is adaptive to the smoothness of the underlying components, and the estimation consistency can reach a parametric rate if the underlying model is really parametric. Simulation studies are conducted to examine the performance of the proposed method. Furthermore, a real data example is analyzed for illustration.

     

Variable selection of generalized regression models based on maximum rank correlation

In this paper, we investigate the variable selection problem of the generalized regression models. To estimate the regression parameter, a procedure combining the rank correlation method and the adaptive lasso technique is developed, which is proved to have oracle properties. A modified IMO （iterative marginal optimization） algorithm which directly aims to maximize the penalized rank correlation function is proposed. The effects of the estimating procedure are illustrated by simulation studies.     

再论线性模型自变元选择的BIC方法相容性条件

在许多情况下，对线性回归模型我们感兴趣于选择足够多的重要预测变量，本文指出了１中对著名的ＢＩＣ准则变量选择方法强相合性证明的错误，并重新给出了一组强相全性条件。在这组条件下，我们也证明了ＢＩＣ选择方法是强相合的，这组新的条件既容易验证又应用广泛。     

Variable Selection in Linear Regression With Many Predictors

With advanced capability in data collection, applications of linear regression analysis now often involve a large number of predictors. Variable selection thus has become an increasingly important issue in building a linear regression model. For a given selection criterion, variable selection is essentially an optimization problem that seeks the optimal solution over 2^m possible linear regression models, where m is the total number of candidate predictors. When m is large, exhaustive search becomes practically impossible. Simple suboptimal procedures such as forward addition, backward elimination, and backward-forward stepwise procedure are fast but can easily be trapped in a local solution. In this article we propose a relatively simple algorithm for selecting explanatory variables in a linear regression for a given variable selection criterion. Although the algorithm is still a suboptimal algorithm, it has been shown to perform well in extensive empirical study. The main idea of the procedure is to partition the candidate predictors into a small number of groups. Working with various combinations of the groups and iterating the search through random regrouping, the search space is substantially reduced, hence increasing the probability of finding the global optimum. By identifying and collecting “important” variables throughout the iterations, the algorithm finds increasingly better models until convergence. The proposed algorithm performs well in simulation studies with 60 to 300 predictors. As a by-product of the proposed procedure, we are able to study the behavior of variable selection criteria when the number of predictors is large. Such a study has not been possible with traditional search algorithms.

This article has supplementary material online.