泊松回归模型中协变量含误差的经验似然推断

Empirical Likelihood Inference for Error-prone Covariates in Poisson Regression Models

在模型的协变量含有测量误差的情况下,考虑一类泊松回归模型的统计推断问题.通过巧妙地构造辅助随机向量,提出一个工具变量类型的经验似然统计推断方法.证明构造的经验对数似然比函数渐近服从标准卡方分布,进而给出了回归系数的置信区间.所提出的估计方法可以有效地消除测量误差对估计精度的影响,并且具有较好的有限样本性质.

The empirical likelihood statistical inference problem of the Poisson regression model is researched in the case of containing measurement error. By cleverly constructed an auxiliary random vector, an instrumental variable type empirical likelihood procedure is proposed. The log likelihood ratio function is shown to be asymptotical standard chi- squared, and then a confidence interval of regression coefficient is given. Some simulation studies show that the proposed method is effective.