面板数据复合分位数回归模型的渐进相对效率
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摘要
针对面板数据个体固定效应复合分位数回归模型,研究回归系数估计的渐进相对效率.采用计算复合分位数回归估计和最小二乘法估计的协方差矩阵的迹的比值,计算结果表明复合分位数回归相对于最小二乘法的渐进相对效率的比值大于70%.还将Zou在2008年提出的适应性lasso的想法应用于此面板数据个体固定效应复合分位数回归模型,构造出适应性lasso惩罚复合分位数回归估计,并在适当条件下证明其估计的渐进性质.
In this paper,the asymptotic relative efficiency of regression coefficient estimation was studied for the composite quantile regression model of individual fixed effect in panel data. The ratio of trace of covariance matrix of composite quantile regression estimation and least squares estimation was calculated. The results showed that the asymptotic phase of composite quantile regression was relative to that of least squares method. The ratio of efficiency to efficiency was more than 70%. This paper also applied Zous idea of adaptive lasso proposed in 2008 to the composite quantile regression model of individual fixed effect in panel data,constructed the adaptive lasso penalty composite quantile regression estimation,and proved the asymptotic nature of the estimation under appropriate conditions.
In this paper,the asymptotic relative efficiency of regression coefficient estimation was studied for the composite quantile regression model of individual fixed effect in panel data. The ratio of trace of covariance matrix of composite quantile regression estimation and least squares estimation was calculated. The results showed that the asymptotic phase of composite quantile regression was relative to that of least squares method. The ratio of efficiency to efficiency was more than 70%. This paper also applied Zous idea of adaptive lasso proposed in 2008 to the composite quantile regression model of individual fixed effect in panel data,constructed the adaptive lasso penalty composite quantile regression estimation,and proved the asymptotic nature of the estimation under appropriate conditions.
引文
[1]王留鑫,洪名勇.我国农业全要素生产率的区域差异及影响因素—基于DEA-Malmquis指数省际面板数据的实证分析[J].郑州航空工业管理学院学报,2018(3):11-21.
[2]朱洋,刘阳.普惠金融发展的贫困减缓效应研究—基于中国省级面板数据的实证[J].金融与经济,2018(5):36-43.
[3] KOENKER,BASSETT. Regression Quantiles[J]. Econometrica,1978,46(1):33-50.
[4] ROGER K. Quantile regression for longitudinal data[J]. Journal of Multivariate Analysis,2004,91(1):74-89.
[5] ZOU H,YUAN M. Composite quantile regression and the oracle model selection theory[J]. The Annals of Statistics,2008(3):1108-1126.
[6]徐洁,杨宜平.面板数据复合分位数回归模型的估计[J].统计与决策,2018(5):19-21.
[7]刘爱义,王松桂.线性模型中最小二乘估计的一种新的相对效率[J].应用概率统计,1989(2):97-104.
[8] POLLARD D. Asymptotic for Least Abslolute Deviation Regression Estimators[M].[S. l.]:Cambridge University Press,1991.
[9] ZHAO K F,LIAN H. A note on the efficiency of composite quantile regression[J]. Journal of Statistical Computation and Simulation,2016(86):1334-1341.
[10]李群峰.基于分位数回归的面板数据模型估计方法[J].统计与决策,2011(17):24-26.
[11]李缓.面板数据分位数回归模型的参数估计与变量选择[D].武汉:武汉科技大学,2015.
[12] JIANG R,QIAN W. Composite quantile regression for nonparametric model with random censored data[J]. Open Journal of Statistics,2013(3):65-73.
[13] KNIGHT K. Limiting distributions for l1 regression estimators under general conditions[J]. The Annals of Statistics,1998(26):755-770.
[14]王琪锋.复合分位数回归在线性时间序列下的应用[D].大连:大连理工大学,2015.
[15] ANTONIO F,GALVAO JR. Quantile regression for dynamic panel data with fixed effects[J]. Journal of Econometrics,2011,164:142-157.
[2]朱洋,刘阳.普惠金融发展的贫困减缓效应研究—基于中国省级面板数据的实证[J].金融与经济,2018(5):36-43.
[3] KOENKER,BASSETT. Regression Quantiles[J]. Econometrica,1978,46(1):33-50.
[4] ROGER K. Quantile regression for longitudinal data[J]. Journal of Multivariate Analysis,2004,91(1):74-89.
[5] ZOU H,YUAN M. Composite quantile regression and the oracle model selection theory[J]. The Annals of Statistics,2008(3):1108-1126.
[6]徐洁,杨宜平.面板数据复合分位数回归模型的估计[J].统计与决策,2018(5):19-21.
[7]刘爱义,王松桂.线性模型中最小二乘估计的一种新的相对效率[J].应用概率统计,1989(2):97-104.
[8] POLLARD D. Asymptotic for Least Abslolute Deviation Regression Estimators[M].[S. l.]:Cambridge University Press,1991.
[9] ZHAO K F,LIAN H. A note on the efficiency of composite quantile regression[J]. Journal of Statistical Computation and Simulation,2016(86):1334-1341.
[10]李群峰.基于分位数回归的面板数据模型估计方法[J].统计与决策,2011(17):24-26.
[11]李缓.面板数据分位数回归模型的参数估计与变量选择[D].武汉:武汉科技大学,2015.
[12] JIANG R,QIAN W. Composite quantile regression for nonparametric model with random censored data[J]. Open Journal of Statistics,2013(3):65-73.
[13] KNIGHT K. Limiting distributions for l1 regression estimators under general conditions[J]. The Annals of Statistics,1998(26):755-770.
[14]王琪锋.复合分位数回归在线性时间序列下的应用[D].大连:大连理工大学,2015.
[15] ANTONIO F,GALVAO JR. Quantile regression for dynamic panel data with fixed effects[J]. Journal of Econometrics,2011,164:142-157.