具有自相关误差结构的面板数据部分线性单指标模型的统计推断

Statistical inference for partially linear single-index model of panel data with serially correlated error structure

部分线性单指标模型是在科学研究中具有广泛应用的经典半参数模型之一.本文主要研究具有自相关误差结构的面板数据的部分线性单指标模型的统计推断问题.通过结合局部多项式和纠偏广义估计方程方法,本文提出模型参数的可行加权广义估计(feasible weighted generalized estimating equation estimation, GEE-FW),证明该估计具有相合性和渐近正态性,并且在渐近方差意义下阐明该估计比工作独立的广义估计(generalized estimating equation estimation based on working independence,GEE-WI)更加有效.此外,本文对模型中未知连接函数提出两阶段局部线性估计(two step local linear generalized estimating equation estimation, GEE-TS),建立该估计的渐近性质.数值模拟研究和实际数据分析都表明了本文所提出的方法是有效的,在理论和应用方面均具有良好的表现.

Due to its flexibility,partially linear single-index model arises in many contemporary scientific endeavor.In this paper,we set foot on its inference under settings of panel data and a serially correlated error component structure.By combining local polynomial technique with the bias-corrected generalized estimating equations,we propose a feasible weighted generalized estimating equation estimation(GEE-FW)for unknown regression parameters.The GEE-FW is shown to be asymptotically normal and more efficient than the unweighted generalized estimating equation estimation based on working independence(GEE-WI).Moreover,a two stage local linear generalized estimating equation estimation(GEE-TS)of the unknown link function is also proposed,which takes the contemporaneous correlation into account and achieves an increase in its estimated efficiency.The asymptotic property of the GEE-TS is established as well and we show that it is asymptotically more efficient than the one which ignores the contemporaneous correlation.Conducted numerical simulation studies and actual data analysis show that the proposed estimate methods are effective and have good performance in both theory and application.