基于纵向数据的半参数变系数部分线性回归模型

纵向数据是数理统计研究中的复杂数据类型之一0,在生物、医学和经济学中具有广泛的应用．在实际中经常需要对纵向数据进行统计分析和建模．文章讨论了纵向数据下的半参数变系数部分线性回归模型,这里的纵向数据的在纵向观察在时间上可以是不均等的,也可看成是按某一随机过程来发生．所研究的半参数变系数模型包括了许多半参数模型,比如部分线性模型和变系数模型等．利用计数过程理论和局部线性回归方法,对于纵向数据下半参数变系数进行了统计推断,给出了参数分量和非参数分量的profile最小二乘估计,研究了这些估计的渐近性质,获得这些估计的相合性和渐近正态性．     

非参数部分带有测量误差的部分线性变系数模型的经验似然推断

研究非参数部分带有测量误差的部分线性变系数模型,构造了模型中未知参数的局部纠偏经验对数似然比统计量,在适当条件下,证明了所提出的统计量具有渐近x2分布,由此结果可以用来构造未知参数的置信域.并且还构造了未知参数的最大经验似然估计及系数函数的估计,证明了它们的渐近性质.最后通过数值模拟研究了所提估计方法在有限样本下的实际...     

缺失数据下半参数变系数部分线性模型的统计推断

该文研究协变量随机缺失下半参数变系数部分线性模型的统计推断.利用逆概率加权最小二乘方法给出了模型中参数分量和非参数分量的估计,并证明了它们的渐近正态性.另外该文又提出了一个逆概率加权经验对数似然比统计量,并证明该统计量服从标准χ~2分布,从而构造了模型中参数分量的经验似然置信域.最后通过模拟研究和实例分析说明该文提出的方法具有较好的有限样本性质.     

部分线性模型的模态正交经验似然推断

本文考虑部分线性模型的有效经验似然统计推断问题.通过结合模态回归和正交投影技术,提出了一种模态经验似然统计推断过程.证明了提出的经验似然比函数渐近服从中心卡方分布,进而构造了模型参数的置信区间.所提出的估计方法可以对模型的参数分量和非参数分量分别估计,而互不影响,具有较好的稳健性和有效性.     

变系数部分线性测量误差模型的B-样条估计（英文）

本文研究变系数部分线性测量误差模型的估计问题.利用纠偏方法,获得参数分量修正的最小二乘估计和非参数分量的B-样条估计.证明参数估计是相合的,渐近正态的;系数函数的B-样条估计达到非参数回归估计的最优收敛速度.模拟结果表明该方法是有效的.     

变系数混合模型的光滑样条推断

为了拟合纵向数据和其他相关数据,本文提出了变系数混合效应模型(VCMM).该模型运用变系数线性部分来表示协变量对响应变量的影响,而用随机效应来描述纵向数据组内的相关性, 因此,该模型允许协变量和响应变量之间存在十分灵活的泛函关系.文中运用光滑样条来估计均值部分的系数函数,而用限制最大似然的方法同时估计出光滑参数和方差成分,我们还得到了所提估计的计算方法.大量的模拟研究表明对于具有各种协方差结构的变系数混合效应模型,运用本文所提出的方法都能够十分有效地估计出模型中的系数函数和方差成分.     

响应变量缺失下变系数部分线性测量误差模型的约束估计

当响应变量缺失、协变量具有测量误差,且模型参数部分有附加的线性约束时,主要研究一类变系数部分线性模型的统计推断问题.利用借补技术来补全缺失数据,并借助修正的profile最小二乘估计得到了模型参数分量和非参数分量的借补约束估计,并证明了参数分量的估计满足渐近正态性,同时非参数分量的估计与通常的非参数回归函数的估计具有相同的收敛速度.其次利用profile拉格朗日乘子检验对模型参数的约束条件进行检验,并证明了给出的检验统计量在原假设成立时渐近地服从标准卡方分布.数值模拟进一步表明对缺失数据进行借补可以有效地提高参数估计和假设检验的效率.     

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.     

泊松回归模型中协变量含误差的经验似然推断

在模型的协变量含有测量误差的情况下,考虑一类泊松回归模型的统计推断问题.通过巧妙地构造辅助随机向量,提出一个工具变量类型的经验似然统计推断方法.证明构造的经验对数似然比函数渐近服从标准卡方分布,进而给出了回归系数的置信区间.所提出的估计方法可以有效地消除测量误差对估计精度的影响,并且具有较好的有限样本性质.     

带有约束的部分线性变系数EV模型的偏差纠正统计推断

本文研究参数和非参数部分均带有测量误差(EV)的部分线性变系数模型的约束统计推断,综合profile最小二乘估计方法和局部纠偏方法给出模型中未知参数和系数函数的两种约束估计,并在适当条件下证明它们的渐近性质.最后通过数值模拟研究所提估计方法在有限样本下的实际表现.     

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 in semiparametric regression analysis for longitudinal data

In this paper, we present a variable selection procedure by using basis function approximations and a partial group SCAD penalty for semiparametric varying coefficient partially linear models with longitudinal data. With appropriate selection of the tuning parameters, we establish the oracle property of this procedure. 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 errors-in-variables models

This paper focuses on the variable selections for semiparametric varying coefficient partially linear models when the covariates in the parametric and nonparametric components are all measured with errors. A bias-corrected variable selection procedure is proposed by combining basis function approximations with shrinkage estimations. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the regularized estimators are established. A simulation study and a real data application are undertaken to evaluate the finite sample performance of the proposed method.     

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.     

Empirical likelihood inferences for semiparametric instrumental variable models

This paper studies the empirical likelihood inferences for a class of semiparametric instrumental variable models. We focus on the case that some covariates are endogenous variables, and some auxiliary instrumental variables are available. An instrumental variable based empirical likelihood method is proposed, and it is shown that the proposed empirical log-likelihood ratio is asymptotically chi-squared. Then, the confidence intervals for the regression coefficients are constructed. Some simulation studies are undertaken to assess the finite sample performance of the proposed empirical likelihood procedure.     

Empirical likelihood for heteroscedastic partially linear models

We make empirical-likelihood-based inference for the parameters in heteroscedastic partially linear models. Unlike the existing empirical likelihood procedures for heteroscedastic partially linear models, the proposed empirical likelihood is constructed using components of a semiparametric efficient score. We show that it retains the double robustness feature of the semiparametric efficient estimator for the parameters and shares the desirable properties of the empirical likelihood for linear models. Compared with the normal approximation method and the existing empirical likelihood methods, the empirical likelihood method based on the semiparametric efficient score is more attractive not only theoretically but empirically. Simulation studies demonstrate that the proposed empirical likelihood provides smaller confidence regions than that based on semiparametric inefficient estimating equations subject to the same coverage probabilities. Hence, the proposed empirical likelihood is preferred to the normal approximation method as well as the empirical likelihood method based on semiparametric inefficient estimating equations, and it should be useful in practice.     

半参数线性混合效应模型的联合变量选择

多数基于线性混合效应模型的变量选择方法分阶段对固定效应和随机效应进行选择,方法繁琐、易产生模型偏差,且大部分非参数和半参数的线性混合效应模型只涉及非参数部分的光滑度或者固定效应的选择,并未涉及非参变量或随机效应的选择。本文用B样条函数逼近非参数函数部分,从而把半参数线性混合效应模型转化为带逼近误差的线性混合效应模型。对随机效应的协方差矩阵采用改进的乔里斯基分解并重新参数化线性混合效应模型,接着对该模型的极大似然函数施加集群ALASSO惩罚和ALASSO惩罚两类惩罚,该法能实现非参数变量、固定效应和随机效应的联合变量选择,基于该法得出的估计量也满足相合性、稀疏性和Oracle性质。文章最后做了个数值模拟,模拟结果表明,本文提出的估计方法在变量选择的准确性、参数估计的精度两个方面均表现较好。     

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.     

一类零膨胀半参数混合效应模型的惩罚似然估计

本文将半参数线性混合效应模型推广应用到一类具有零膨胀的纵向数据或集群数据的研究中,提出了一类新的半参数混合效应模型,然后利用广义交叉核实法选取光滑参数,通过最大惩罚似然函数方法与EM算法给出了模型参数部分与非参数部分的估计方法,最后,通过模拟和实例说明了本文方法的有效性.