动态变系数回归模型的识别与非参数GMM估计

Nonparametric GMM and Model Identification in Dynamic Varying Coefficient Regression Models

主要研究关于面板数据的有限阶固定效应的动态变系数回归模型(简称FDVCM)的统计推断问题.基于B-样条函数和广义矩估计(简称GMM)方法,首先建立了未知系数函数的非参数GMM估计,并证明大样本情形下该估计达到最优非参数收敛速度且具有渐近正态性质.然而实际问题中模型的动态阶数完全未知,也可能存在其它冗余的回归变量,文中借助文[Fan J,Li R.Variable selection via penalized likelihood and its oracle properties.Journal of the American Statistical Association,2001,96(456):1348-1360]中的smoothly clipped absolute deviation(简称SCAD)惩罚函数同时识别真实的动态阶数和显著的外生回归变量.同时建立了压缩估计的Oracle性质,即所识别的模型与真实模型中的参数估计具有相同的渐近分布.最后,无论是数值试验还是实例数据分析都验证了本文方法的合理性和可行性.

This paper focuses on the fixed effects dynamic varying coefficient regression model（FDVCM for short） for panel data with finite autoregressive lag order.Applying Bspline series approximation and generalized method-of-moment（GMM for short） techniques,the authors construct the nonparametric GMM estimators of unknown coefficient functions firstly.These estimators not only achieve the optimal nonparametric convergence rate but are shown to have asymptotic normality distribution.In practice,the lag order is often unknown.Misspecification of the order will lead to biased estimators and unreliable inferences.Then the authors further propose a unified penalised GMM procedure by employing the smoothly clipped absolute deviation（SCAD for short）（see[Fan J,Li R.Variable selection via penalized likelihood and its oracle properties.Journal of the American Statistical Association,2001,96（456）：1348-1360]） penalty to identify the true lag order and significant exogenous variables simultaneously.It＇s shown that the shrinking estimators have oracle property in the sense that the selected significants have the same asymptotic property as if nonzero coefficient functions are known in advance.Both numerical experiments and real data application illustrate the performance of our approach.