异方差模型中协方差阵的估计研究
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摘要
在异方差模型中,尽管回归系数的普通最小二乘(OLS)估计仍能保持无偏性,但其对应的协方差阵估计不再一致。解决异方差问题,对随机误差项协方差阵的估计显得尤为重要。基于异方差形式未知的情况下,非参数估计的良好效果,应用不同的非参数方法对误差项的协方差阵给出估计,进而通过估计加权最小二乘法得到回归系数的估计,并在已有的加权异方差一致协方差阵估计的基础上进行了拓展。模拟实验和实例分析表明,不同的非参数方法在回归系数的估计和模型的检验方面效果都有很大的差异。
In the heteroscedasticity model,although the ordinary least squares( OLS) estimator of the regression coefficient can still remain unbiased,its corresponding covariance matrix estimator is no longer consistent. To solve the heteroskedastic problem,it is especially important to estimate the covariance matrix of random error terms. Based on the excellent effect of the non-parametric estimation when the form of heteroscedasticity is unknown,different non-parametric methods are used to estimate the covariance matrix of the error terms and then the regression coefficient is estimated by the estimated weighted least squares method. Some weighted heteroskedasticity consistent covariance matrix estimations are extended on the basis of it. Simulation experiments and a case study show that different nonparametric methods have great differences in the estimation of regression coefficients and the effects of model test.
In the heteroscedasticity model,although the ordinary least squares( OLS) estimator of the regression coefficient can still remain unbiased,its corresponding covariance matrix estimator is no longer consistent. To solve the heteroskedastic problem,it is especially important to estimate the covariance matrix of random error terms. Based on the excellent effect of the non-parametric estimation when the form of heteroscedasticity is unknown,different non-parametric methods are used to estimate the covariance matrix of the error terms and then the regression coefficient is estimated by the estimated weighted least squares method. Some weighted heteroskedasticity consistent covariance matrix estimations are extended on the basis of it. Simulation experiments and a case study show that different nonparametric methods have great differences in the estimation of regression coefficients and the effects of model test.
引文
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[2]邓明,王劲波.误差合成空间固定系数模型的多阶段广义最小二乘估计[J].数理统计与管理,2016,35(1):57-70.
[3]WANG C,QI F,SHI G,et al.A linear combination-based weighted least square approach for target localization with noisy range measurements[J].Signal Processing,2014,94(1):202-211.
[4]胡俊航,焦勇.线性约束下异方差回归模型参数的极大似然估计[J].数学的实践与认识,2014,44(16):117-121.
[5]CARROLL R J.Adapting for heteroscedasticity in linear models[J].Annals of Statistics,1982,10(4):1224-1233.
[6]FURNO M.Small sample behavior of a robust heteroskedasticity consistent covariance matrix estimator[J].Journal of Statistical Computation&Simulation,2012,54(1-3):115-128.
[7]ASLAM M,PASHA G R.Adaptive estimation of heteroscedastic linear regression models using heteroscedasticity consistent covariance matrix[J].Journal of Statistics,2009,16:28-44
[8]WHITE H.A heterokedasticity-consistent a variance matrix estimator and a direct test for heterokedasticity[J].Econome-trica,1980,48(4):817-827.
[9]HAYES A F,LI C.Using heteroskedasticity consistent standard error estimators in OLS regression:An introduction and software implementation[J].Behavior Research Methods,2007,39(4):709.
[10]CRIBARI-NETO F.Asymptotic inference under heteroskedasticity of unknown form[J].Computational Statistics&Data Analysis,2004,45(2):215-233.
[11]CRIBARI-NETO F,SOUZA T C,VASCONCELLOS K LP.Inference under heteroskedasticity and leveraged data[J].Communications in Statistics,2007,36(10):1877-1888.
[12]CRIBARINETO 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):129-146.
[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):198-210.
[14]MUNIR A,MUHAMMAD A,PASHA G R.Inference under heteroscedasticity of unknown form using an adaptive estimator[J].Communications in Statistics,2011,40(24):4431-4457.
[15]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,2003,12(2):153-156.
[16]仝倩,冯予.带缺失数据的半参数非线性模型基于经验似然的统计诊断[J].贵州师范大学学报(自然科学版),2017,35(4):89-94.
[17]LIMA V C,SOUZA T,FRANCISCO C N,et al.Heteroskedasticity robust inference in linear regressions[J].Communications in Statistics Simulation and Computation,2009,39(1):194-206.
[18]王彤.线性回归模型的稳健估计及多个异常点诊断方法研究[D].西安:第四军医大学,2000.