Frequentist model averaging for linear mixed-effects models

Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.     

广义线性模型(十)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分3部分:建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L.Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(八)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分3部分:建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L.Fahrmeir等人的《MultivariateStatisticalModel ingBasedonGeneralizedLinearModels》     

广义线性模型(三)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(二)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(一)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

Randomly censored partially linear single-index models

This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure-time models for survival analysis. The estimation procedure involves three stages: first, transform the censored data into synthetic data or pseudo-responses unbiasedly; second, obtain quasi-likelihood estimates of the regression coefficients in both linear and single-index components by an iteratively algorithm; finally, estimate the unknown nonparametric regression function using techniques for univariate censored nonparametric regression. The estimators for the regression coefficients are shown to be jointly root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as all the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodology.     

BLUP estimation of linear mixed-effects models with measurement errors and its applications to the estimation of small areas

The linear mixed-effects model （LMM） is a very useful tool for analyzing cluster data. In practice, however, the exact values of the variables are often difficult to observe. In this paper, we consider the LMM with measurement errors in the covariates. The empirical BLUP estimator of the linear combination of the fixed and random effects and its approximate conditional MSE are derived. The application to the estimation of small area is provided. Simulation study shows good performance of the proposed estimators.     

Precise asymptotics of error variance estimator in partially linear models

In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression models, y _i = x _i ^τ β + g(t _i ) + ε _i , 1 ≤ i ≤ n, {ε _i , i = 1, ⋯ n} are i.i.d random errors with mean 0 and positive finite variance σ ². Following the ideas of Allan Gut and Aurel Spătaru^[7,8] and Zhang^[21], on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.      

Generalized linear models for the analysis of taguchi-type experiments

Recent interest in Taguchi's methods have led to developments in joint analysis of the mean and dispersion from designed experiments. A commonly used method is the analysis of variance of the transformed data. However, a single transformation cannot necessarily produce the Normality, constancy of variance and linearity of systematic effects for the mean and dispersion models. We describe the use of generalized linear models for the analysis of such experiments and illustrate the methods with a data set.     

Generalized linear models for dependent frequency and severity of insurance claims

Traditionally, claim counts and amounts are assumed to be independent in non-life insurance. This paper explores how this often unwarranted assumption can be relaxed in a simple way while incorporating rating factors into the model. The approach consists of fitting generalized linear models to the marginal frequency and the conditional severity components of the total claim cost; dependence between them is induced by treating the number of claims as a covariate in the model for the average claim size. In addition to being easy to implement, this modeling strategy has the advantage that when Poisson counts are assumed together with a log-link for the conditional severity model, the resulting pure premium is the product of a marginal mean frequency, a modified marginal mean severity, and an easily interpreted correction term that reflects the dependence. The approach is illustrated through simulations and applied to a Canadian automobile insurance dataset.     

Asymptotic properties in semiparametric partially linear regression models for functional data

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.     

Bayesian hierarchical linear mixed models for additive smoothing splines

Bayesian hierarchical models have been used for smoothing splines, thin-plate splines, and L-splines. In analyzing high dimensional data sets, additive models and backfitting methods are often used. A full Bayesian analysis for such models may include a large number of random effects, many of which are not intuitive, so researchers typically use noninformative improper or nearly improper priors. We investigate propriety of the posterior for these cases. Our findings extend known results for normal linear mixed models to certain cases with Bayesian additive smoothing spline models. Supported by National Science Foundation grant SES-0351523 and by National Institutes of Health grants R01-CA100760 and R01-MH071418.     

响应变量存在缺失时部分线性模型的经验似然推断

考虑响应变量带有缺失的部分线性模型,采用借补的思想,研究了参数部分和非参数部分的经验似然推断,证明了所提出的经验对数似然比统计量依分布收敛到χ2分布,由此构造参数部分和函数部分的置信域和逐点置信区间.对参数部分,模拟比较了经验似然与正态逼近方法;对函数部分,模拟了函数的逐点置信区间.     

Covariate Selection in High-Dimensional Generalized Linear Models With Measurement Error

In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several recent papers have studied methods which correct for measurement error in the lasso or Dantzig selector for linear models in the p > n setting. We study a correction for generalized linear models, based on Rosenbaum and Tsybakov’s matrix uncertainty selector. By not requiring an estimate of the measurement error covariance matrix, this generalized matrix uncertainty selector has a great practical advantage in problems involving high-dimensional data. We further derive an alternative method based on the lasso, and develop efficient algorithms for both methods. In our simulation studies of logistic and Poisson regression with measurement error, the proposed methods outperform the standard lasso and Dantzig selector with respect to covariate selection, by reducing the number of false positives considerably. We also consider classification of patients on the basis of gene expression data with noisy measurements. Supplementary materials for this article are available online.     

Double penalized variable selection procedure for partially linear models with longitudinal data

Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.     

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.     

纵向数据下非参数带测量误差的部分线性变系数模型的估计

本文研究纵向数据下非参数部分带有测量误差的部分线性变系数模型的估计.利用B样条函数近似模型中的变系数函数,构造偏差修正的二次推断函数,得到模型中未知参数和变系数函数的估计.证明变系数函数估计量的相合性和参数估计量的渐近正态性.数值模拟和实例分析结果表明所提估计方法在有限样本下的有效性.     

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.     

Efficient estimation for semiparametric varying- coefficient partially linear regression models with current status data

This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.