部分函数型EV回归模型的经验似然推断

Empirical Likelihood Inference of Partial Function EV Regression Model

针对解释变量带有测量误差的部分函数型线性回归模型,引入一个合适辅助向量,构造出未知参数的经验对数似然比函数,给出了未知参数和未知系数的极大经验似然估计。进一步证明了所构造似然比函数具有渐近卡方分布,并基于此构造了未知参数的渐近置信域。同时,也证明了给出的未知参数的估计与最小二乘估计一样具有渐近正态性。最后给出系数函数的收敛速度,达到了最优收敛速度。讨论的结果说明经验似然方法对部分函数型EV回归模型的统计推断是有效的。

The purpose of this paper is to study the partial functional linear regression model with measurement errors in explanatory variables.An appropriate auxiliary vector is introduced to construct the empirical log-likelihood ratio function of unknown parameters,and the maximum empirical likelihood estimates of unknown parameters and unknown coefficients are given.It is further proved that the constructed likelihood ratio function has an asymptotic chi-square distribution,and based on this,an asymptotic confidence region of unknown parameters is constructed.At the same time,the asymptotic normality of the estimation of unknown parameters is proved as that of least squares estimation.Finally,the convergence rate of coefficient function is given,and the optimal convergence rate is achieved.The results show that empirical likelihood method is effective for statistical inference of partial functional EV regression models.