带约束推断的参数和半参数回归模型有偏估计及变量选择理论与方法研究

项目名称： 带约束推断的参数和半参数回归模型有偏估计及变量选择理论与方法研究

项目编号： No.11201505

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 黎雅莲

作者单位： 重庆大学

项目金额： 22万元

中文摘要： 本项目研究带约束推断的参数和半参数回归模型有偏估计及其变量选择理论与方法。首先，对于参数和半参数回归模型中的复共线性问题，研究在带约束推断下的有偏估计方法；当约束条件不值得信任时，进一步研究参数基于Wald、LR和LM检验等大样本检验的预检验估计，并重点研究其大样本下的统计性质。其次，对复杂数据类型的半参数回归模型，应用经验对数似然和调整经验似然检验方法进行经验似然比统计推断。最后，研究如何利用Boosting等方法来实现估计的变量选择，其中重点研究约束有偏估计中偏参数和LASSO类方法中光滑参数的选取问题，以及相应估计在大样本下的相合性、渐近正态性和置信区间推断等问题。

中文关键词： 约束有偏估计；预检验估计；纵向数据；模型选择；

英文摘要： The theory and methods of biased estimation and variable selection in restricted inference parametric and semiparametric regression models are studied in this project. Firstly, when there exists multicollinearity in parametric and semiparametric regression model, the restricted biased estimators are studied; when the constraints are not be trusted, further research about the preliminary test estimators which parameters based on large sample test such as Wald, LR and LM test, and keypoint its large sample of the statistical properties. Second, for the semiparametric regression models with complex data, we apply the experience logarithm likelihood and adjusted empirical likelihood methods to make empirical likelihood ratio statistical inference. Finally, the study how to use methods such as Boosting method to achieve the variable selection of estimation, of which mainly research the selection of the partial parameters in the restricted biased estimators and the smooth parameters in the LASSO class methods, as well as the corresponding estimators under large smaple which properties such as consistency, asymptotic normality and confidence interval inference.

英文关键词： Restricted biased estimation；Preliminary test estimator；Longitudinal data；Model selection；