摘要
在右删失数据下,研究了误差具有异方差结构的非参数回归模型,利用局部多项式方法构造了回归函数的加权局部复合分位数回归估计,并得到了该估计的渐近正态性结果,最后通过模拟,当误差为重尾分布时,该估计比局部多项式估计以及核估计表现得更好.
In this paper, the nonparametric regression model with heteroscedastic error is considered under right-cesored data. Based on the local polynomial method, a weighted local composite quantile regression estimator of regression function is constructed. Under appropriate assumptions,the asymptotic normality of the estimator is also established. The simulation studies show that the paper's estimators perform better than the local polynomial estimator and the kernel estimation when the error is the heavy tail distribution.
引文
[1] Nadaraya E A. On estimating regression[J]. Theory Probab Appl, 1964, 9:141-142.
[2] Fan Jianqing, Gijbels I. Variable bandwidth and local linear regression smoothers[J]. Ann Statist, 1992, 4:2008-2036.
[3] Kai Bo, Li Runze, Zou Hui. Local composite quantile regression smoothing:an efficient and safe alternative to local polynomial regression[J]. J Roy Statist Soc Ser B, 2010, 72:49-69.
[4] Fan Jianqing, Gi.jbels I. Censored regression:local linear approximations and their applications[J]. J Amer Statist Assoc, 1994, 89:560-570.
[5] Guessoum Z, Ould-Said E. On nonparametric estimation of the regression function under random censorship model[J]. Statist Decisions, 2008, 26:159-177.
[6] Guessoum Z, Ould-Said E. Central limit theorem for the kernel estimator of the regression function for censored time series[J]. J Nonparametr Stat, 2012, 24:379-397.
[7] Tang Linjun, Zhou Zhougong, Wu Changchun. Weighted composite quantile estimation and variable selection method for censored regression model[J]. Statist Probab Lett, 2012, 82:653-663.
[8] Kaplan E L, Meier P. Nonparametric Estimation from Incomplete Observations[J]. J Amer Statist Assoc, 1958, 53:457-481.
[9] Fan Jianqing. Design-adaptive nonparametric regression[J]. J Amer Statist Assoc, 1992, 87:998-1004.
[10] Loprinzi C L, Laurie J A, Wieand H S, et al. Prospective evaluation of prognostic variables from patient-completed questionnaires. North central cancer treatment group[J]. J Clinical Oncology, 1994, 12:601-607.
[11] Knight K. Limiting distributions for L_1 regression estimators under general conditions[J].Ann Statist, 1998, 26:755-770.
[12] Parzen E. On estimation of a probability density function and model[J]. Ann Math Statist,1962, 33:1065-1076.
[13] Fldes A, Rejto L. Strong uniform consistency for nonparametric survival curve estimators from randomly censored data[J]. Ann Statist, 1981, 19:135-144.
[14] Koenker R. Quantile Regression[M]. Cambridge:Cambridge University Press, 2015.
