Panel Count Data模型参数的经验似然推断

The Empirical Likelihood Inference of Parameters in the Panel Count Data Model

对Panel Count Data的处理越来越受到人们的关注,Sun与Wei^([1-2])基于简单的半参数模型,提出了Panel Count Data的回归分析,并且给出了参数的估计方程。本文则基于经验似然的思想,讨论了上述Panel Count Data模型参数的置信域构造问题,特别仅通过经验似然置信区域给出了参数估计的方差阵估计,证明了估计的1/n相合性。基于Sun与Wei所给的数据,给出了参数置信区域的具体构造过程和结果。通过作图比较可以看出经验似然置信域要优于依据渐近正态性所构造的置信域。我们还依据所作出的经验似然置信域对参数估计的方差矩阵进行了估计,与用传统渐近正态性得到的矩阵较为接近。

It is payed more attention to deal with the panel count data. Sun and Wei[1-2] gave a regressive result on panel count data based on the semi-parameter model and then they implied the estimation equations of the parameters. However they didn＇t consider to construct the confidence regions of parameters. We try to solve this problem in this paper, and construct the empirical likelihood confidence regions for the parameters based on the Sun and Wei＇s estimation equations. Meanwhile, the covariance matrix estimation of parameter estimate is given based on only the empirical likelihood confidence regions. For tbe real data, it is shown that the empirical likelihood confidence regions are better than the traditional confidence regions by the asymptotic normality approach. Moreover, the variance matrices of parameter estimates are given by use of the empirical likelihood confidence regions.