Abstract

In this paper, the empirical likelihood-based inference is investigated with varying coefficient panel data models with fixed effect. A naive empirical likelihood ratio is firstly proposed after the fixed effect is corrected. The maximum empirical likelihood estimators for the coefficient functions are derived as well as their asymptotic properties. Wilk’s phenomenon of this naive empirical likelihood ratio is proven under a undersmoothing assumption. To avoid the requisition of undersmoothing and perform an efficient inference, a residual-adjusted empirical likelihood ratio is further suggested and shown as having a standard chi-square limit distribution, by which the confidence regions of the coefficient functions are constructed. Another estimators for the coefficient functions, together with their asymptotic properties, are considered by maximizing the residual-adjusted empirical log-likelihood function under an optimal bandwidth. The performances of these proposed estimators and confidence regions are assessed through numerical simulations and a real data analysis.

摘要

在本文中，使用具有固定效应的可变系数面板数据模型研究了基于经验似然的推理。在修正固定效应后，首先提出一个朴素的经验似然比。导出了系数函数的最大经验似然估计量以及它们的渐近特性。Wilk 的这种朴素经验似然比的现象在不平滑的假设下得到证明。为了避免欠平滑的要求并执行有效的推理，进一步建议了残差调整的经验似然比，并显示为具有标准的卡方极限分布，通过该分布构造系数函数的置信区域。系数函数的另一个估计量，连同它们的渐近性质，通过在最佳带宽下最大化残差调整的经验对数似然函数来考虑。这些提议的估计器和置信区域的性能通过数值模拟和真实数据分析进行评估。