删失指标随机缺失下一类非参数函数的加权局部多项式估计及其应用  

Weighted Local Polynomial Estimations of a Non-parametric Function with Censoring Indicators Missing at Random and Their Applications

作　　者：王江峰[1] 周杨程 唐菊 WANG Jiangfeng;ZHOU Yangcheng;TANG Ju(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou,Zhejiang,310018,P.R.China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018

出　　处：《数学进展》2020年第4期463-480,共18页Advances in Mathematics（China）

基　　金：国家社会科学基金(No.16BTJ029);浙江省自然科学基金(No.LY18A010007)。

摘　　要：本文在右删失数据中删失指标部分随机缺失下,构造了一类非参数函数的校准加权局部多项式估计以及插值加权局部多项式估计,并建立了这些估计的渐近正态性;作为该方法的应用,导出了条件分布函数、条件密度函数以及条件分位数的加权局部线性双核估计和插值加权局部线性双核估计,并且得到了这些估计的渐近正态性;最后,在有限样本下对这些估计进行了模拟.In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random,and establish the asymptotic normality of these estimators.As their applications,we derive the weighted local linear estimator and imputation estimation of the conditional distribution function,the conditional density function and the conditional quantile function,and investigate the asymptotic normality of these estimators.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators.

关 键 词：局部多项式估计 渐近正态性 非参数函数 删失指标 随机缺失 

分 类 号：O212.7[理学—概率论与数理统计]