纵向数据单指标模型中参数的经验似然置信域

Empirical Likelihood Confidence Regions of the Parameters in Single-Index Models for Longitudinal Data

考虑纵向数据单指标模型,针对纵向数据组间独立的特点,提出了模型中未知参数的三种经验对数似然比统计量.在适当条件下,证明了所提出的统计量依分布收敛于x^2分布,所得结果可以构造未知参数的置信域.进一步证明了所提出的纠偏的经验对数似然比有许多优良的性质.通过模拟研究对所提方法进行了说明.

In this paper,the single-index model for longitudinal data is considered,three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested to accommodate the independence of different subjects for longitudinal data.It is proved that the proposed statistics are asymptotically chisquare distribution under some suitable conditions,and hence they can be used to construct the confidence regions of the parameters.Furthermore,it is shown that the bias corrected empirical log-likelihood ratio shares some desired features.A simulation study is conducted to illustrate our methods.