联合广义线性模型中的变量选择

在联合广义线性模型中,散度参数与均值都被赋予了广义线性模型的结构,本文主要考虑在只有分布的一阶矩和二阶矩指定的条件下,联合广义线性模型中均值部分的变量选择问题。本文采用广义拟似然函数,提出了新的模型选择准则(EAIC);该准则是Akaike信息准则的推广。论文通过模拟研究验证了该准则的效果。     

Finite Mixture of Generalized Semiparametric Models: Variable Selection via Penalized Estimation

Selection of the important variables is one of the most important model selection problems in statistical applications. In this article, we address variable selection in finite mixture of generalized semiparametric models. To overcome computational burden, we introduce a class of variable selection procedures for finite mixture of generalized semiparametric models using penalized approach for variable selection. Estimation of nonparametric component will be done via multivariate kernel regression. It is shown that the new method is consistent for variable selection and the performance of proposed method will be assessed via simulation.     

Variable Selection in Joint Location and Scale Models of the Skew-t-Normal Distribution

Variable selection is an important issue in all regression analysis, and in this article, we investigate the simultaneous variable selection in joint location and scale models of the skew-t-normal distribution when the dataset under consideration involves heavy tail and asymmetric outcomes. We propose a unified penalized likelihood method which can simultaneously select significant variables in the location and scale models. Furthermore, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the location and scale models. With appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. These estimators are compared by simulation studies.     

Robust Variable Selection in Linear Mixed Models

In this article, we develop a robust variable selection procedure jointly for fixed and random effects in linear mixed models for longitudinal data. We propose a penalized robust estimator for both the regression coefficients and the variance of random effects based on a re-parametrization of the linear mixed models. Under some regularity conditions, we show the oracle properties of the proposed robust variable selection method. Simulation study shows the robustness of the proposed method against outliers. In the end, the proposed methods is illustrated in the analysis of a real data set.     

Variable Selection for Partially Linear Models with Randomly Censored Data

This article proposes a variable selection procedure for partially linear models with right-censored data via penalized least squares. We apply the SCAD penalty to select significant variables and estimate unknown parameters simultaneously. The sampling properties for the proposed procedure are investigated. The rate of convergence and the asymptotic normality of the proposed estimators are established. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to have the asymptotic oracle property. In addition, an iterative algorithm is proposed to find the solution of the penalized least squares. Simulation studies are conducted to examine the finite sample performance of the proposed method.     

Lack-of-Fit Tests for Generalized Linear Models via Splines

Cubic B-splines are used to estimate the nonparametric component of a semiparametric generalized linear model. A penalized log-likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the nonparametric function. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one df. The smoothing parameter is determined by giving a specified value for its asymptotically expected value under the null hypothesis. A simulation study is conducted to evaluate its power performance; a real-life dataset is used to illustrate its practical use.     

Tuning Parameter Selection in Penalized Frailty Models

The penalized likelihood approach of Fan and Li (2001 Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Association 96:1348–1360.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 2002 Fan, J., Li, R. (2002). Variable selection for Cox’s proportional hazards model and frailty model. The Annals of Statistics 30:74–99.[Crossref], [Web of Science ®] , [Google Scholar]) differs from the traditional variable selection procedures in that it deletes the non-significant variables by estimating their coefficients as zero. Nevertheless, the desirable performance of this shrinkage methodology relies heavily on an appropriate selection of the tuning parameter which is involved in the penalty functions. In this work, new estimates of the norm of the error are firstly proposed through the use of Kantorovich inequalities and, subsequently, applied to the frailty models framework. These estimates are used in order to derive a tuning parameter selection procedure for penalized frailty models and clustered data. In contrast with the standard methods, the proposed approach does not depend on resampling and therefore results in a considerable gain in computational time. Moreover, it produces improved results. Simulation studies are presented to support theoretical findings and two real medical data sets are analyzed.     

Smooth-Threshold GEE Variable Selection in High-Dimensional Partially Linear Models with Longitudinal Data

We consider the problem of variable selection in high-dimensional partially linear models with longitudinal data. A variable selection procedure is proposed based on the smooth-threshold generalized estimating equation (SGEE). The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimates the nonzero regression coefficients by solving the SGEE. We establish the asymptotic properties in a high-dimensional framework where the number of covariates p_n increases as the number of clusters n increases. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure.     

Robust Estimation in Binary Choice Models

The binary-response smoothed maximum score (SMS) estimator accommodates heteroskedasticity of an unknown form, but it may be heavily biased when the conditional error density is not differentiable or not bell shaped. We construct a new combined SMS estimator as a linear combination of individual estimators with weights chosen to minimize the trace of estimated mean squared error. This estimator is robust and rate-adaptive under weak assumptions on the density. Results of a Monte Carlo study confirm good performance of the combined estimator.     

A Numerical Study of PQL Estimation Biases in Generalized Linear Mixed Models Under Heterogeneity of Random Effects

The penalized quasi-likelihood (PQL) approach is the most common estimation procedure for the generalized linear mixed model (GLMM). However, it has been noticed that the PQL tends to underestimate variance components as well as regression coefficients in the previous literature. In this article, we numerically show that the biases of variance component estimates by PQL are systematically related to the biases of regression coefficient estimates by PQL, and also show that the biases of variance component estimates by PQL increase as random effects become more heterogeneous.     

Variable Selection for Semiparametric Partially Linear Covariate-Adjusted Regression Models

In this article, the partially linear covariate-adjusted regression models are considered, and the penalized least-squares procedure is proposed to simultaneously select variables and estimate the parametric components. The rate of convergence and the asymptotic normality of the resulting estimators are established under some regularization conditions. With the proper choices of the penalty functions and tuning parameters, it is shown that the proposed procedure can be as efficient as the oracle estimators. Some Monte Carlo simulation studies and a real data application are carried out to assess the finite sample performances for the proposed method.     

Rate of Strong Consistency of Maximum Quasi-Likelihood Estimator in Multivariate Generalized Linear Models

In this article, we consider a multivariate generalized linear model with adaptive design matrix and general link function. The asymptotic singularity of design matrix of adaptive design presents challenge when establishing the large sample properties of the maximum quasi-likelihood estimate (MQLE). Under some mild conditions, we obtain a strong convergence rate of the MQLE.     

Tuning Parameter Selector for the Penalized Likelihood Method in Multivariate Generalized Linear Models

Variable selection is fundamental to high-dimensional multivariate generalized linear models. The smoothly clipped absolute deviation (SCAD) method can solve the problem of variable selection and estimation. The choice of the tuning parameter in the SCAD method is critical, which controls the complexity of the selected model. This article proposes a criterion to select the tuning parameter for the SCAD method in multivariate generalized linear models, which is shown to be able to identify the true model consistently. Simulation studies are conducted to support theoretical findings, and two real data analysis are given to illustrate the proposed method.     

Linear Transformations of Linear Mixed-Effects Models

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.     

Variable Selection in Linear Mixed Models Using an Extended Class of Penalties

There is an emerging need to advance linear mixed model technology to include variable selection methods that can simultaneously choose and estimate important effects from a potentially large number of covariates. However, the complex nature of variable selection has made it difficult for it to be incorporated into mixed models. In this paper we extend the well known class of penalties and show that they can be integrated succinctly into a linear mixed model setting. Under mild conditions, the estimator obtained from this mixed model penalised likelihood is shown to be consistent and asymptotically normally distributed. A simulation study reveals that the extended family of penalties achieves varying degrees of estimator shrinkage depending on the value of one of its parameters. The simulation study also shows there is a link between the number of false positives detected and the number of true coefficients when using the same penalty. This new mixed model variable selection (MMVS) technology was applied to a complex wheat quality data set to determine significant quantitative trait loci (QTL).     

New Robust Variable Selection Methods for Linear Regression Models

Motivated by an entropy inequality, we propose for the first time a penalized profile likelihood method for simultaneously selecting significant variables and estimating unknown coefficients in multiple linear regression models in this article. The new method is robust to outliers or errors with heavy tails and works well even for error with infinite variance. Our proposed approach outperforms the adaptive lasso in both theory and practice. It is observed from the simulation studies that (i) the new approach possesses higher probability of correctly selecting the exact model than the least absolute deviation lasso and the adaptively penalized composite quantile regression approach and (ii) exact model selection via our proposed approach is robust regardless of the error distribution. An application to a real dataset is also provided.     

Exponential-Bound Property of Estimators and Variable Selection in Generalized Additive Models

In this article, utilizing a scale mixture of skew-normal distribution in which mixing random variable is assumed to follow a mixture model with varying weights for each observation, we introduce a generalization of skew-normal linear regression model with the aim to provide resistant results. This model, which also includes the skew-slash distribution in a particular case, allows us to accommodate and detect outlying observations under the skew-normal linear regression model. Inferences about the model are carried out through the empirical Bayes approach. The conditions for propriety of the posterior and for existence of posterior moments are given under the standard noninformative priors for regression and scale parameters as well as proper prior for skewness parameter. Then, for Bayesian inference, a Markov chain Monte Carlo method is described. Since posterior results depend on the prior hyperparameters, we estimate them adopting the empirical Bayes method as well as using a Monte Carlo EM algorithm. Furthermore, to identify possible outliers, we also apply the Bayes factor obtained through the generalized Savage-Dickey density ratio. Examining the proposed approach on simulated instance and real data, it is found to provide not only satisfactory parameter estimates rather allow identifying outliers favorably.     

基于分层广义线性模型的非寿险费率厘定精算模型研究

非寿险业务中的损失数据结构日益复杂,呈现异质性与相关性并存的异象。分层广义线性模型能够突破传统费率厘定精算方法仅分析风险个体同一保单年损失数据的局限,可以提高复杂结构损失数据预测的准确性。基于分层广义线性模型等方法,研究具有多年损失数据的非寿险费率厘定问题,并以车险和工伤补偿保险的两组损失数据为例进行实证分析。研究结果表明,相对于GLM而言,考虑随机效应后GLMM的拟合优度大幅改善,GLMM与HGLM可以更有效地反映不同风险个体的差异,并有利于揭示风险个体在多个保险期内损失的异质性与相关性。     

Empirical Likelihood-Based Inferences for Generalized Partially Linear Models

Abstract.  This paper considers generalized partially linear models. We propose empirical likelihood-based statistics to construct confidence regions for the parametric and non-parametric components. The resulting statistics are shown to be asymptotically chi-square distributed. Finite-sample performance of the proposed statistics is assessed by simulation experiments. The proposed methods are applied to a data set from an AIDS clinical trial.     

广义线性模型在非寿险精算中的应用及其研究进展

广义线性模型在精算中的应用始于20世纪80年代，其应用涉及到精算学的各个领域，如生命表的修匀、损失分布、信度理论、风险分类、准备金和费率估计等方面。在对广义线性模型适用于非寿险精算的典型特征进行分析的基础上，对广义线性模型在非寿险精算中的应用及其研究进展进行分析和总结的同时，重点分析利率厘定和准备金估计中广义线性模型的建模思想，并结合实际提出了今后研究的方向。