Asymptotic normality of Powell’s kernel estimator

被引：0
作者：
Kengo Kato
机构：
[1] Hiroshima University,Department of Mathematics, Graduate School of Science
来源：
Annals of the Institute of Statistical Mathematics | 2012年 / 64卷
关键词：
Asymptotic normality; Bandwidth selection; Censored quantile regression; Density estimation; Kernel method; Quantile regression;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the approximate mean squared error of the kernel estimator. We also derive the corresponding results to censored quantile regression.
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页码：255 / 273
页数：18
相关论文
共 43 条
[1]  
Ahmad I.A.(1992)Residual density estimation in nonparametric regression Statistics and Probability Letters 14 133-139
[2]  
Andrews D.W.K.(1991)Heteroskedasticity and autocorrelation consistent covariance matrix estimation Econometrica 59 817-858
[3]  
Angrist J.(2006)Quantile regression under misspecification, with an application to the U.S. wage structure Econometrica 74 539-563
[4]  
Chernozhukov V.(1994)Central limit theorems for empirical and U-processes of stationary mixing sequences Journal Theoretical Probability 7 47-71
[5]  
Fernandéz-Val I.(1975)Estimation of a density function using order statistics Australian Journal of Statistics 17 1-7
[6]  
Arcones M.A.(1993)Asymptotic theory for estimation of error distributions of linear model Science in China Series A 36 408-419
[7]  
Yu B.(1991)Consistent nonparametric estimation of error distributions in linear model Acta Mathematicae Applicatae Sinica 7 245-256
[8]  
Bofinger E.(2002)Consistency of error density and distribution function estimators in nonparametric regression Statistics and Probability Letters 59 257-270
[9]  
Chai G.X.(2004)Weak and strong uniform consistency of a kernel error density estimator in nonparametric regression Journal of Statistical Planning and Inference 119 95-107
[10]  
Li Z.Y.(2005)Asymptotic distributions of error density and distribution function estimators in nonparametric regression Journal of Statistical Planning and Inference 128 327-349
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