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.     

基于生存数据的半参数变换的删失回归估计

生存数据经过未知的单调变换后等于协变量的线性函数加上随机误差, 随机误差的分布函数已知或是带未知参数的已知函数\bd 本文先给出未知单调变换的一个相合估计, 再对删失数据做变换, 在此基础上给出了协变量系数的最小二乘估计, 并讨论它的大样本性质.     

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.     

带有误差变量混合分布模型的估计

在许多实际同题中，存在一些不可直接观测的变量，对此统计学家们提出了反卷积和混合分布模型来解决这一变量的分布的估计问题。本文对这一问题采用bootstrap模拟方法得出分布函数的估计，并进一步建立该分布函数的非参bootstrap百分位区间，在数值试验中将我们的处理方式与传统的EM算法得到的分布估计和正态逼近区间作比较，数值结果表明用bootstrap模拟方法得到的准确度更好，数值效果更理想。     

超高维Ⅱ型区间删失数据的非参数变量筛选法北大核心CSCD

在定期随访的医学研究或临床实验中,人们经常会收集到高维区间删失数据,如何对这类数据进行降维是一个非常有意义的问题.本文基于Kolmogorov-Smirnov检验统计量,利用分割和融合的技巧,把独立特征筛选方法推广到区间删失数据中,提出了一种可以处理超高维Ⅱ型区间删失数据且不依赖于任何模型假设的变量筛选方法.此方法的适用范围很广,可以有效地处理各种生存模型下的超高维Ⅱ型区间删失数据,而且可以处理离散型,连续型等多种类型的协变量.在估计生存函数时,本文采用EM-ICM算法,极大地提高了计算效率.大量的数值模拟实验验证了此方法在有限样本下的有效性.     

竞争风险下纵列持续数据随机效应模型的估计与模拟研究

本文论证竞争风险下纵列持续数据随机效应模型属于广义线性模型的范畴,推导出用于模型估计的等级似然函数,将等级似然估计的运用由单风险扩展到竞争风险,并进行了模拟研究。模拟结果表明,对于竞争风险下的随机效应模型,等级似然估计能够给出协变量系数相当精确的估计,克服了忽略异质性影响所导致的偏差;模拟研究还表明,本文提出的估计方法同样适用于区间观测数据。     

成分数据的几个估计

本文用SURE模型导出了成分数据的均值和协差阵的估计。特别地，在成分数据服从Dirichlet分布D（a1,…,ad 1)时,构造了参数a=∑j=1^d 1 aj的二次估计及a1,…,ad 1的三次估计，求出了这些估计的渐近分布。     

BurrTypeXⅡ分布的统计推断

该文讨论了两参数BurrTypeXⅡ分布基于逐次定数截尾样本的参数估计，导出了有关参数的点估计和区间估计．我们利用模拟方法对所给点估计和参数的最大似然估计作了比较，模拟结果显示所给点估计优于常用的最大似然估计．最后，用一个实际例子说明本文所给方法．     

指数分布场合下基于分组数据和双向册失数据的区间估计

当寿命分布是指数分布时本文给出了基于分组数据和双向册失数据平均寿命的近似区间估计方法，所给方法的计算是简单的。     

区间数据任意阶原点矩的估计

在生存分析和可靠性研究中, 区间数据的存在常常使得传统的统计方法无法直接使用\bd 本文从无偏转换的思想出发, 对区间数据的任意阶原点矩进行了估计\bd 当截断变量的分布密度函数已知时, 得到了一批具有强相合性(收敛速度可以达到$n^{-1/2}(\log\log n)^{1/2}$)和渐近正态性的估计量, 并通过模拟计算对这种估计方法的可行性和有效性进行了验证.     

A moving window approach for nonparametric estimation of the conditional tail index

We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations. This selection is achieved through a moving window approach on the covariate domain and a random threshold on the variable of interest. Asymptotic normality is proved under mild regularity conditions and illustrated for some weight functions. Finite sample performances are presented on a real data study.     

Generalized Partially Linear Measurement Error Models

This article considers generalized partially linear models when the linear covariate is measured with additive error. We propose estimators of parameter and nonparametric function by using local linear regression, the SIMEX technique, and generalized estimating equation. The asymptotic normality of the estimators of the parameter, and bias and variance of the estimators of the nonparametric component are derived under appropriate assumptions. In addition, the generalization to clustered measurements is discussed. The approaches are used to the analysis of data from the Framingham Heart Study. A simulation experiment is conducted for an illustration.     

Multivariate logistic regression with incomplete covariate and auxiliary information

In this article, we propose and explore a multivariate logistic regression model for analyzing multiple binary outcomes with incomplete covariate data where auxiliary information is available. The auxiliary data are extraneous to the regression model of interest but predictive of the covariate with missing data. Horton and Laird [N.J. Horton, N.M. Laird, Maximum likelihood analysis of logistic regression models with incomplete covariate data and auxiliary information, Biometrics 57 (2001) 34–42] describe how the auxiliary information can be incorporated into a regression model for a single binary outcome with missing covariates, and hence the efficiency of the regression estimators can be improved. We consider extending the method of [9] to the case of a multivariate logistic regression model for multiple correlated outcomes, and with missing covariates and completely observed auxiliary information. We demonstrate that in the case of moderate to strong associations among the multiple outcomes, one can achieve considerable gains in efficiency from estimators in a multivariate model as compared to the marginal estimators of the same parameters.     

Estimating parameters in one-way analysis of covariance model with short-tailed symmetric error distributions

We consider one-way analysis of covariance (ANCOVA) model with a single covariate when the distribution of error terms are short-tailed symmetric. The maximum likelihood (ML) estimators of the parameters are intractable. We, therefore, employ a simple method known as modified maximum likelihood (MML) to derive the estimators of the model parameters. The method is based on linearization of the intractable terms in likelihood equations. Incorporating these linearizations in the maximum likelihood, we get the modified likelihood equations. Then the MML estimators which are the solutions of these modified equations are obtained. Computer simulations were performed to investigate the efficiencies of the proposed estimators. The simulation results show that the proposed estimators are remarkably efficient compared with the conventional least squares (LS) estimators.     

变系数线性EV模型参数的调整加权最小二乘估计及其渐近性质

研究当结构关系EV(errors-in-variables)模型的系数随某个实变量变化时,如何估计其系数,以及估计的性质如何．采用调整的加权最小二乘方法估计结构关系EV模型的变系数,证明在比较弱的条件下用这种方法得到的估计具有强相合性和渐近正态性,模拟研究表明所提估计性质良好．     

A class of weighted estimating equations for additive hazard models with covariates missing at random

Missing covariate data arise frequently in biomedical studies. In this article, we propose a class of weighted estimating equations for the additive hazard regression model when some of the covariates are missing at random. Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations. Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modeling schemes. The resulting estimators have closed forms and are shown to be consistent and asymptotically normal. Simulation studies indicate that the proposed estimators perform well for practical settings. An application to a mouse leukemia study is illustrated.

     

Fixed Design Nonparametric Regression with Truncated and Censored Data

In this paper we consider a fixed design model in which the observations axe subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covaxiate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator.Applications include trimmed mean and quantile function estimators.     

带有辅助信息的多元失效时间数据的估计标准部分似然方法

在许多实际研究中, 由于预算限制, 主协变量值只能对某一个有效集进行准确测量, 但同时对应此主协变量的辅助信息则对全部个体均可以观测. 利用这些辅助协变量的信息有助于提高统计研究的效率. 本文在基于共同基准危险率的边际模型框架下, 我们提出了一些统计推断方法来分析多元失效时间数据. 对于回归参数, 我们提出标准的估计部分似然方程来估计它, 同时也给出了累积基准危险率函数的Breslow 型估计. 得到的估计可以证明是相合的和渐近正态的. 利用模拟分析结果来表明了提出的方法在有限样本下的可行性.     

多类型复发事件下变系数加性乘积比率回归模型

本文基于多类型复发事件数据,讨论了一个新的加性乘积比率回归模型,该模型包括两部分,其中第一部分为可加Aalen模型,其中协变量影响为加性的且与时间有关.第二部分为Cox回归模型,其中协变量有乘性影响.利用估计方程的方法,给出了该模型中未知参数和非参数函数的一种估计方法,并利用现代经验过程理沦证明了所得估计的相合性和渐近正态性.     

Testing a sub-hypothesis in linear regression models with long memory covariates and errors

This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be n ^1/2-consistent for all values of the long memory parameters of the design and error processes. Research of the first author was partly supported by the NSF DMS Grant 0701430. Research of the second author was partly supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State Science and Studies Foundation grant T-15/07.