流行病学中若干统计分析模型的推断

项目名称： 流行病学中若干统计分析模型的推断

项目编号： No.11271039

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 张忠占

作者单位： 北京工业大学

项目金额： 60万元

中文摘要： 有形状约束的统计推断和变量挑选都是统计推断中的重要课题。本项目研究的问题主要集中在两个方面：第一是流行病学或医学试验中某些非随机缺失机制下有约束的统计推断，包括(A.1) 半参数模型或非参数模型中非参数部分有形状约束的问题的估计和检验. 结合不同的试验数据类型和不同的模型，研究有形状约束的条件下非参数部分的估计和检验问题。在估计问题中，在数据缺失的情况下如何构造相合估计是要讨论的主要问题；而对于检验问题，主要是构造具有较高功效的检验，并给出p值的计算方法。 (A.2) 有关序问题的假设检验。我们将研究数据具有缺失时，离散型分布（在生物医学研究中十分常用）和连续型分布模型下的多种序的检验。第二是复杂模型的变量选择，包括(B.1) 均值方差（散度）联合模型的变量挑选；(B.2) 在B1的基础上，对于因果分析模型中的变量选择进行研究，力争提出能够用于因果分析的变量挑选准则。

中文关键词： 变量选择；M估计；Bayes推断；形状约束；随机序

英文摘要： The goals of the research of the project are mainly set on the following two aspects. The first is on shape constrained statistical inference in the cases that some kind of nonrandom missing exists. Shape constrained statistical inference is often concerned with in epidemiology studies or clinical trials. There are two problems are focused: (A.1) Estimation and test where there is a shape constraint for the nonparametric fanction in the semiparametric model or nonparametric model considered. We shall study the estimation and test for the shape constrained nonparametric functions combining with different kinds of data and models. For estimation, the main target is to construct an efficient consistent estimator, and for test problem, the main target will be put on how to construct a powerful test and how to compute its p values or critical values. (A.2) Test for given order constraints of distributions. We shall study the order constraint tests with missing data for both discrete distributions and continuous distributions in the sense of, for instance, stochastic order and likelihood ratio order. The second aspect is on variable selection in complicated models. Two kinds of problems are focused for the second aspect: (B.1) simultaneousely variable selection in the joint regression models for mean and variance (d

英文关键词： variable selection；M estimation；Bayesian inference；shape restriction；stochastic order