H广义线性模型中的参数估计的比较

本文研究H广义线性模型中未知参数的两种估计方法，一种是边际似然函数法，另一种是Lee和Nelder提出来的L-N法．对于一类具有两个随机效应的典型的Poisson-Gamma类模型，在一些正则性条件之下，我们已经证明了其中固定效应卢的L-N估计的强相合性及渐近正态性，并得到了其收敛于真值的速度．针对这类模型，本文进一步给出了其边际似然函数的解析表达式，并且通过Monte Carlo模拟，对模型中固定效应β的边际似然估计和L—N估计进行了比较，模拟表明L—N估计比边际似然估计在拟Poisson-Gamma模型中有着更加优良的表现，具有更高的精度。

Comparison of the Parameter Estimators in Hierarchical Generalized Linear Models

In this paper, we are focused on the estimation of parameters in hierarchical generalized linear models. Based on the large sample properties proved by authors, Monte Carlo Simulation method is employed to compare L-N estimator and maximum marginal likelihood estimator for small and moderate sample sizes in an extended Poisson-Gamma model family. It is shown that the L-N estimator appears much better than the maximum marginal likelihood estimator, which is difficult to implement because of the integration involved.