纵向数据单指标模型的广义经验似然统计推断

Generalized Empirical Likelihood Inference for Single-index Models

基于广义估计方程和二次推断函数方法,提出了纠偏的广义经验似然方法对纵向数据单指标模型进行统计推断,获得了模型中指标参数分量的极大经验似然估计和纠偏的广义经验对数似然比统计量.证明了相关估计量在一定条件下具有渐近正态性,且纠偏的广义经验对数似然比统计量依分布收敛于χ2分布,利用所得结果,可以构造未知参数的置信域及相关的假设检验.

Based on the generalized estimation equations （ GEE ） and the quadratic inference functions （ QIF ） methods, a bias-corrected generalized empirical likelihood was proposed to make statistical inference for the single-index model with longitudinal data. The maximum empirical likelihood estimator and the bias-corrected generalized empirical log-likelihood ratio statistics for the unknown index parameter in the model were obtained. It is proved that the maximum empirical likelihood estimator is asymptotically normal and the proposed statistics are asymptotically chi-square distributed under certain conditions, and hence they can be applied to construct the confidence region of the index parameter.