广义线性模型中基于拟似然的变量选择方法

变量选择是建立广义线性模型的基础．为了选择变量，本文提出了一种惩罚拟似然方法．这种方法不需要知道数据的分布，而只要求知道数据的一二阶矩．在统计推断过程中，此方法同时进行变量选择和参数估计，得到估计具有Oracle性质，并是渐近有效的．同时，本文定义了一种后验拟似然，于是，选择变量的过程就是一个比较拟后验密度的过程．特别的，对于线性模型，比较拟后验密度就等价于比较惩罚残差平方和．

Variable Selection Based on Quasi Likelihood for Generalized Linear Models

Variable selection is foundation for linear models. To this goal, this paper proposes a penalized quasi likelihood. The new method does not depend on the distribution of data rather than on the first two moments. The method in the procedure of inference selects variables and estimates parameters simultaneously. The resulting estimators have the Oracle property and are asymptotically efficient. Also a posterior likelihood is introduced and then the procedure of selecting changes to be a procedure of comparing the posterior density. Particularly, for linear models, comparing the posterior density is equivalent to comparing penalized residual sum of squares.