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

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.

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。

本项目主要研究了参数和半参数回归模型中未知参数的约束有偏估计及其变量选择理论。首先针对统计线性模型中的复共线性问题，深入研究了模型在等式约束和随机约束推断下的有偏估计方法，重点研究双参数估计、r-k估计和r-d估计等;当对约束条件是否成立不确定时，进一步研究参数基于大样本检验的预检验估计。其次，针对半参数回归模型，研究参数的差分岭估计和差分Liu估计并讨论其统计性质,构造了关于部分线性可加模型的参数和非参函数部分的稳健变量选择方法。此外，对具有纵向数据复杂数据类型的回归模型，讨论了未知参数基于广义估计方程的稳健推断。本项目资助在境外SCI期刊录用发表论文共计11篇。