| 李 睿,郝瑞丽.动态变系数回归模型的识别与非参数GMM估计[J].数学年刊A辑,2016,37(3):337~358 |
| 动态变系数回归模型的识别与非参数GMM估计 |
| Nonparametric GMM and Model Identificationin Dynamic Varying Coefficient Regression Models |
| Received:September 10, 2013 Revised:June 28, 2015 |
| DOI： |
| 中文关键词: 变系数模型, 动态回归, 样条近似, 惩罚GMM估计, Oracle性质 |
| 英文关键词:Varying coefficient model, Dynamic regression, Spline approximation, Penalized GMM estimate, Oracle property |
| 基金项目:本文受到国家自然科学基金 (No.11471203), 中国博士后基金 (No.2014M551297),
上海市教委科研创新项目 (No.13YZ125)和上海财经大学优秀博士论文培育基金 (No.14110045)的资助. |
| Author Name | Affiliation | | LI Rui | Corresponding author. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433
School of Business Information, Shanghai University of
International Business and Economics, Shanghai 201620, China. | | HAO Ruili | Post-doctoral station of Applied Economics, Fudan University, Shanghai 200433
School of Statistics and Mathematics, Shanghai Finance University, Shanghai 201209
Shanghai Key Laboratory of Financial Information Technology
(Shanghai University of Finance and Economics), Shanghai 200433, China. |
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| 中文摘要: |
| 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.
{\it 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. |
| 英文摘要: |
| This paper focuses on the fixed effects dynamic varying coefficient
regression model (FDVCM for short) for panel data with finite autoregressive lag order.
Applying B-spline 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.
{\it 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. |
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