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分位数回归是均值回归的有益补充,该方法毋须对分布函数的具体形式做出假设,且对具有异常值或厚尾分布的数据仍具有稳健性。当前,对部分线性单指数面板模型估计方法的研究主要集中于均值回归,基于此,本文考虑了固定效应部分线性单指数面板分位数回归模型,结合B-样条函数、SCAD惩罚函数和迭代加权最小二乘法,构建了模型的估计方法,证明了估计方法的一致性和渐近正态性,同时利用Monte Carlo模拟评价了所述方法在有限样本下的表现。最后,将估计方法应用于分析碳排放的影响因素。
Abstract：Quantile regression is a useful supplement to mean regression. The method needn't assume specification of distribution and is robust to outlie or heavy tail distribution of data. Most previous studies on partially linear single index models concentrated on mean regression. Based on this,this paper investigated quantile regression of partially linear single index panel models with fixed effect. We estimated the model based on the combination of B spline function,SCAD penalized function and reweighted least squares algorithm,and proved the consistence and asymptotic normality of estimators. Also,we evaluated the finite sample performance of the proposed method via Monte Carlo simulation. Furthermore,the proposed method is illustrated in factor analysis of carbon emissions.
[1]Fan J,Gijbels I.Local Polynomial Modelling and Its Applications[M].London:Chapman and Mall Publishing,1997.1-304.
[2]Gao J.Nonlinear Time Series:Semiparametric and Nonparametric Methods[M].Australia:Chapman and Mall Publishing,2007.1-198.
[3]Li Q,Racine J S.Nonparametric Econometrics:Theory and Practice[M].New Jersey:Princeton University Press Publishing,2007.1-348.
[4]Lin D Y,Ying Z.Semiparametric and Nonparametric Regression Analysis of Longitudinal Data[J].Journal of the American Statistical Association,2001(96):103-113.
[5]Su L,Ullah A.Profile Likelihood Estimation of Partially Linear Panel Data Models with Fixed Effects[J].Economics Letters,2006(92):75-81.
[6]Li G,Tian P,Xue,L.Generalized Empirical Likelihood Inference in Semiparametric Regression Model for Longitudinal Data[J].Acta Mathematica Sinica,2008(24):2029-2040.
[7]Qian J,Wang L.Estimating Semiparametric Panel Data Models by Marginal Integration[J].Journal of Econometrics,2012(167):483-493.
[8]Chen J,Gao J,Li D.Estimation in Partially Linear Single-Index Panel Data Models with Fixed Effect[J].Journal of Business and Economic Statistics,2013(31):315-330.
[9]Fan J,Hu T,Truong Y.Robust Non-Parametric Function Estimation[J].Journal of Statistics,1994(21):433-446.
[10]Wu T,Yu K,Yu Y.Single Index Quantile Regression[J].Journal of Multivariate Analysis,2010(101):1607-1621.
[11]Zhao W,et al.Varible Selection of the Quantile Varying Coefficient Regression Models[J].Journal of the Korean Statistical Society,2013(42):343-358.
[12]Lv Y,et al.Quantile Regression and Variable Selection of Partial linear Single Index Model[J].Annals of the Institute of Statistical Mathematics,2015(67):375-409.
[13]He X,Zhu Z,Fung W.Estimation in a Semiparametric Model for Longitudinal Data with Unspecified Dependence Structure[J].Biometrika,2002(89):579-590.
[14]Wei Y,He X.Discussion Paper Conditional Growth Charts[J].the Annals of Statistics,2006(34):2069-2097.
[15]Wang H J,Zhu Z,Zhou J.Quantile Regression in Partially Linear Varying Coefficient Models[J].the Annals of Statistics,2009(37):3841-3866.
[16]Tang Y,Wang H J,Zhu Z.Variable Selection in Quantile Varying Coefficient Models with Longitudinal data[J].Computational Statistics and Data Analysis,2013(57):435-449.
[17]Wang K,Lin L.Variable Selection in Robust Semiparametric Modeling for Longitudinal Data[J].Journal of the Korean Statistical Society,2014(43):303-314.
[18]Koenker R.Quantile Regression for Longitudinal Data[J].Journal of Multivariate Analysis,2004(91):74-89.
[19]Fan J,Li R.Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties[J].Journal of the American Statistical Association,2001(96):1348-1360.
[20]Ruppert D,Wand M P,Carroll R J.Semiparametric Regression[M].London:Cambridge University Press,2007.112-131.
[21]He X,Shi P.Convergence Rate of B-Spline Estimators of Nonparametric Conditional Quantile Functions[J].Journal of Nonparametric Statistics,2001(3):299-308.
(1)本文将面板数据与纵向数据视为同一类数据。
(1)限于篇幅,未能给出定理证明的细节,有兴趣的读者可向作者索要。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2017.02.010
中图分类号:F224
引用信息:
[1]丁飞鹏.固定效应部分线性单指数面板模型的惩罚分位数回归[J].统计研究,2017,34(02):101-109.DOI:10.19343/j.cnki.11-1302/c.2017.02.010.
2017-02-15
2017-02-15