一种异方差模型的两阶段估计
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摘要
在异方差线性回归模型中,当模型误差项的协方差阵未知时,对异方差模型进行估计目前还没有比较好的方法。基于此,提出一种异方差模型的两阶段估计—基于异方差一致协方差阵估计,该方法将异方差一致协方差阵估计HC5m和广义最小二乘估计法结合起来,综合使用全部样本的信息,并对异方差模型进行估计。通过大量的蒙特卡洛数值模拟和实证分析,结果表明该方法具有一定的可行性和有效性。
In the heteroskedastic linear regression model,when the covariance matrix of the error term of the model is unknown,there are no better methods to estimate the heteroskedastic model.Based on this,a two-stage estimator of the heteroskedastic model is proposed,based on heteroskedastic consistent covariance matrix estimates(HCCME).This method combines the heteroskedastic consistent covariance matrix estimation HC5 m and the generalized least squares(GLE)estimate method,using the entire information of the sample to estimate the heteroskedastic model.According to a large number of Monte Carlo numerical simulations and empirical analysis,the results show that the method has certain feasibility and effectiveness.
In the heteroskedastic linear regression model,when the covariance matrix of the error term of the model is unknown,there are no better methods to estimate the heteroskedastic model.Based on this,a two-stage estimator of the heteroskedastic model is proposed,based on heteroskedastic consistent covariance matrix estimates(HCCME).This method combines the heteroskedastic consistent covariance matrix estimation HC5 m and the generalized least squares(GLE)estimate method,using the entire information of the sample to estimate the heteroskedastic model.According to a large number of Monte Carlo numerical simulations and empirical analysis,the results show that the method has certain feasibility and effectiveness.
引文
[1]Box G E P,Cox D R.An Analysis of Transformation(With Discussion)[J].Journal of the Royal Statistieal Society:Series B,1964(26).
[2]Su L,Zhao Y,Yan T,et al.Local Polynomial Estimation ofHeteroscedasticity in a Multivariate Linear Regression Model and Its Applications in Economics[J].Plos One,2012,7(9).
[3]何其祥,郑明.一元线性模型异方差的局部多项式回归[J].系统管理学报,2003(2).
[4]Zhang X,Hao H,Liang J.A New Nonparametric Estimation Method of the Variance in a Heteroscedastic Model[J].Hacettepe Journal of Mathematics and Statistics,2015,44(1).
[5]张荷观.基于分组的异方差检验和两阶段估计[J].数量经济技术经济研究,2006(1).
[6]李顺勇,钱宇华,张晓琴,等.基于变量选择和聚类分析的两阶段异方差模型估计[J].应用概率统计,2018(2).
[7]White H.A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity[J].Econometrica,1980,48(4).
[8]Hinkley,David V.Jackknifing in Unbalanced Situations[J].Technometrics,1977,19(3).
[9]Horn S D,Horn R A,Duncan D B,et al.Estimating Heteroscedastic Variances in Linear Models[J].Journal of the American Statistical Association,1975,70(350).
[10]Long J S,Ervin L H.Using Heteroskedasticity:Consistent Standard Errors in Linear Regression Model[J].American Statistician,2000,54(3).
[11]Cribari-Neto F.Asymptotic Inference Under Heteroskedasticity of Unknown Form[J].Computational Statistics&Data Analysis,2004,45(2).
[12]Cribari-Neto F,Silva W B D.A New Heteroskedasticity-Consistent Covariance Matrix Estimator for the Linear Regression Model[J].Asta Advances in Statistical Analysis,2011,95(2).
[13]Li S,Zhang N,Zhang X,et al.A New Heteroskedasticity-Consistent Covariance Matrix Estimator and Inference under Heteroskedasticity[J].Journal of Statistical Computation&Simulation,2016,87(1).
[14]格林,张成思.计量经济分析[M].北京:中国人民大学出版社,2011.
(1)此评价指标进行的是横向比较,即在相同的情况下不同方法间的优劣比较。
(2)同上。
(1)此处假设是为了满足使用分组两阶段法时的需要。
[2]Su L,Zhao Y,Yan T,et al.Local Polynomial Estimation ofHeteroscedasticity in a Multivariate Linear Regression Model and Its Applications in Economics[J].Plos One,2012,7(9).
[3]何其祥,郑明.一元线性模型异方差的局部多项式回归[J].系统管理学报,2003(2).
[4]Zhang X,Hao H,Liang J.A New Nonparametric Estimation Method of the Variance in a Heteroscedastic Model[J].Hacettepe Journal of Mathematics and Statistics,2015,44(1).
[5]张荷观.基于分组的异方差检验和两阶段估计[J].数量经济技术经济研究,2006(1).
[6]李顺勇,钱宇华,张晓琴,等.基于变量选择和聚类分析的两阶段异方差模型估计[J].应用概率统计,2018(2).
[7]White H.A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity[J].Econometrica,1980,48(4).
[8]Hinkley,David V.Jackknifing in Unbalanced Situations[J].Technometrics,1977,19(3).
[9]Horn S D,Horn R A,Duncan D B,et al.Estimating Heteroscedastic Variances in Linear Models[J].Journal of the American Statistical Association,1975,70(350).
[10]Long J S,Ervin L H.Using Heteroskedasticity:Consistent Standard Errors in Linear Regression Model[J].American Statistician,2000,54(3).
[11]Cribari-Neto F.Asymptotic Inference Under Heteroskedasticity of Unknown Form[J].Computational Statistics&Data Analysis,2004,45(2).
[12]Cribari-Neto F,Silva W B D.A New Heteroskedasticity-Consistent Covariance Matrix Estimator for the Linear Regression Model[J].Asta Advances in Statistical Analysis,2011,95(2).
[13]Li S,Zhang N,Zhang X,et al.A New Heteroskedasticity-Consistent Covariance Matrix Estimator and Inference under Heteroskedasticity[J].Journal of Statistical Computation&Simulation,2016,87(1).
[14]格林,张成思.计量经济分析[M].北京:中国人民大学出版社,2011.
(1)此评价指标进行的是横向比较,即在相同的情况下不同方法间的优劣比较。
(2)同上。
(1)此处假设是为了满足使用分组两阶段法时的需要。