不完全数据下广义半参数可加模型的统计推断

项目名称： 不完全数据下广义半参数可加模型的统计推断

项目编号： No.11301351

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 张娟

作者单位： 首都经济贸易大学

项目金额： 22万元

中文摘要： 本项目拟研究不完全数据下广义半参数可加模型的统计推断问题。广义半参数可加模型涵盖了多种常见模型，它既保持了模型的可解释性，又兼顾了模型的灵活性，还能避免"维数祸根"，具有广泛的应用范围。在实际应用中经常会出现不完全的数据，比如缺失数据和删失数据。如果不考虑数据的缺失或者删失，将导致信息损失甚至会得到有偏的结论，因此在不完全数据下考虑广义半参数可加模型的统计推断问题是重要而且有意义的。本项目旨在研究因变量随机缺失时，协变量中存在分类变量时广义半参数可加模型的参数和非参数部分的估计及其渐近性质、参数部分经验似然置信区间的构造、参数和非参数部分的同时变量选择等统计推断问题，以及I型区间删失数据下协变量中存在分类变量时半参数可加Cox模型的参数和非参数部分的同时变量选择。最后还将通过数值模拟和实际数据来展示所给方法的效果。

中文关键词： 广义半参数可加模型；不完全数据；假设检验；变量选择；

英文摘要： In this project, we are going to study the statistical inference for the generalized semiparametric additive model with incomplete data. Generalized semiparametric additive model covers many common models. It maintains the interpretability and flexibility of models and avoids "the curse of dimensionality", featuring extensive range of application. In practical application, incomplete data is very common. For example, missing data and censored data. Ignoring these incomplete data can result in the loss of information or even the appearance of a biased conclusion. Therefore, it is of great significance to take into account the treatment of incomplete data in the generalized semiparametric additive model. This project will focus on the situation in which the dependent variable is missing at random and covarites include category variables. Given this situation, we will discuss a series of statistical inferences, including the estimation and asymptotic properties of parametric component and nonparametric component in the generalized semiparametric additive model, the empirical likelihood confidence intervals of the parametric component, the simultaneous variable selection of parametric component and nonparametric component, and we will discuss the variable selection of the semiparametric additive Cox model with curre

英文关键词： generalized semi-parametric additive model；incomplete data；hypothesis test；variable selection；