带有缺失数据的广义半参数模型的均值借补估计

本文在响应变量随机缺失时, 给出了广义半参数模型中响应变量的2个均值拟似然借补估计.证明了它们具有渐近正态性, 给出了估计的渐近偏差与渐近方差, 并进行模拟比较.     

广义线性模型参数的自适应拟似然估计

对广义线性模型参数的一种拟似然估计的理论给予了彻底的处理. 在该估计中,响应变量的未知的协方差阵是通过样本去估计的.证明了所定义的估计量具有下述意义上的渐近有效性：当样本量n→∞时, 该估计有渐近正态性,且其极限分布的协方差阵重合于当响应变量的协方差阵完全已知时,拟似然估计的极限分布的协方差阵.     

基于遍历函数型数据条件风险率函数的核估计

探究了在平稳遍历函数型数据下条件风险率函数的非参数核估计问题,本文基于N-W核估计的方法,构造响应变量Y在给定函数型解释变量X下的条件风险率函数非参数核估计,在一定条件下获得条件风险率函数非参数估计的偏差表达式.     

响应变量随机缺失下的半参变系数模型的均值估计

在响应变量随机缺失时,研究了半参数变系数模型响应变量均值的借补估计.首先利用完整个体估计模型中的参数与非参数部分,然后再用借补方法与加权借补方法估计响应变量的均值.最后求出了估计的渐近偏差与渐近方差,研究了所得到的估计的渐近性质,并进行模拟比较.     

协变量维数可以趋于无穷的纵向数据的广义估计方程分析

广义估计方程(GEE)是分析纵向数据的常用方法.Balan,Schiopu-Kratina(2005)研究了协变量维数固定,GEE估计的渐近正态性.WANG(2011)研究了协变量维数趋于无穷,GEE估计的渐近正态性和响应变量是两点分布Wald统计量的渐近分布.本文证明协变量维数是固定的或趋于无穷,响应变量是任意分布的Wald统计量的渐近分布是卡方分布,Wald统计量可以直接用于统计推断.     

纵向多分类数据的广义估计方程分析

广义估计方程(GEE)是分析纵向数据的常用方法.如果响应变量的维数是一, XIE和YANG(2003)及WANG(2011)分别研究了协变量维数是固定的和协变量维数趋于无穷时, GEE估计的渐近性质.本文研究纵向多分类数据(multicategorical data)的GEE建模和GEE估计的渐近性质.当数据的分类数大于二时,响应变量的维数大于一,所以推广了文献的相关结果.     

基于双变量Probit模型的间隙零门功能可靠性分析

爆炸间隙零门功能的实现,不仅与间隙的长度有关,还受控制通道截面积的影响.如何量化分析间隙零门功能可靠性与间隙长度及截面积的关系是工程技术领域关心的重要问题.综合考虑间隙长度、截面积及其交互影响,基于三元响应,提出了间隙零门成功响应的双变量Probit模型.利用得分统计量,分析了检验双变量Probit模型中两随机误差变量相关性的方法.同时还基于极大似然估计并结合双变量Probit模型,给出了模型参数的估计方法.最后基于一组模拟试验数据,利用双变量Probit模型,给出了该组数据下模型参数的估计结果以及间隙零门功能可靠性窗口的区域分布.     

单调缺失机制下高维纵向线性回归模型的变量选择

在响应变量带有单调缺失的情形下考虑高维纵向线性回归模型的变量选择.主要基于逆概率加权广义估计方程提出了一种自动的变量选择方法,该方法不使用现有的惩罚函数,不涉及惩罚函数非凸最优化的问题,并且可以自动地剔除零回归系数,同时得到非零回归系数的估计.在一定正则条件下,证明了该变量选择方法具有Oracle性质.最后,通过模拟研究验证了所提出方法的有限样本性质.     

关于广义线形回归参数极大似然估计相合性的若干问题

本文在广义线性回归中响应变量服从指数型分布且有自然联系的情况下, 讨论了 模型参数的极大似然估计的相合性条件有关的若干问题.     

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.     

复杂设计下类均值复制与类加权均值复制的比较（英文）

复制数据是处理抽样调查中数据项目缺失的一种常用方法。在两种常见模型及复杂抽样设计下，本文对处理数据项目缺失的类均值复制和类加权均值复制方法进行了对比。     

具有缺失数据的Eichhorn模型

为了解决在Eichhorn乘法扰动模型中存在的项目无回答问题,对敏感变量总体均值在辅助变量总体均值已知与未知条件下提出了比率插补方法.理论比较和数值模拟得出的结果表明提出的插补方法比传统的方法效率更高.     

Quasi-likelihood estimation of average treatment effects based on model information

In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.     

Data-driven local bandwidth selection for additive models with missing data

This paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable. Specifically in the case of additive models estimated by the Backfitting algorithm with local polynomial smoothers [1]. Three estimators are presented, one based on the available data and two based on a complete sample from imputation techniques. We also develop a data-driven local bandwidth selector based on a Wild Bootstrap approximation of the mean squared error of the estimators. The performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments.     

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators.     

Imputation of mean of ratios for missing data and its application to PPSWR sampling

In practical survey sampling, nonresponse phenomenon is unavoidable. How to impute missing data is an important problem. There are several imputation methods in the literature. In this paper, the imputation method of the mean of ratios for missing data under uniform response is applied to the estimation of a finite population mean when the PPSWR sampling is used. The imputed estimator is valid under the corresponding response mechanism regardless of the model as well as under the ratio model regardless of the response mechanism. The approximately unbiased jackknife variance estimator is also presented. All of these results are extended to the case of non-uniform response. Simulation studies show the good performance of the proposed estimators.     

Hazard function estimation with cause-of-death data missing at random

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.     

Sample rotation theory with missing data

This paper studies how the sample rotation method is applied to the case where item non-response occurs in surveys. The two cases where the response to the first occasion is complete or incomplete are considered. Using ratio imputation method, the estimators of the current population mean are proposed, which are valid under uniform response regardless of the model and under the ratio model regardless of the response mechanism. Under uniform response, the variances of the proposed estimators are derived. Interestingly, although their expressions are similar, the estimator for the case of incomplete response on the first occasion can have smaller variance than the one for the case of complete response on the first occasion under uniform response. The linearized jackknife variance estimators are also given. These variance estimators prove to be approximately design-unbiased under uniform response. It should be noted that similar property on variance estimators has not been discussed in literature.