Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors

被引:14
作者
Horrigue, Walid [1 ,2 ]
Said, Elias Ould [1 ,2 ]
机构
[1] Univ Lille Nord France, F-59000 Lille, France
[2] ULCO, LMPA, F-62228 Calais, France
关键词
Censored data; conditional distribution function; infinite dimension; Kaplan-Meier; estimator; kernel estimator; small-ball probability;
D O I
10.1515/ROSE.2011.008
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Let. (T, C, X) be a vector of random variables (rvs) where T, C and X are the interest variable, a right censoring rv and a covariate, respectively. In this paper, we study the kernel conditional quantile estimation in the dependent case and when the covariable takes values in an infinite-dimension space. An estimator of the conditional quantile is given and, under some regularity conditions, among which the small-ball probability for the covariate, its uniform strong convergence with rates is established.
引用
收藏
页码:131 / 156
页数:26
相关论文
共 57 条
[1]  
Bahi M. El, 2008, 382 LMPA ULCO
[2]  
BERAN R., 1981, TECHNICAL REPORT
[3]   Asymptotic normality of convergent estimates of conditional quantiles [J].
Berlinet, A ;
Gannoun, A ;
Matzner-Lober, E .
STATISTICS, 2001, 35 (02) :139-169
[4]   KERNEL AND NEAREST-NEIGHBOR ESTIMATION OF A CONDITIONAL QUANTILE [J].
BHATTACHARYA, PK ;
GANGOPADHYAY, AK .
ANNALS OF STATISTICS, 1990, 18 (03) :1400-1415
[5]   GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY [J].
BOLLERSLEV, T .
JOURNAL OF ECONOMETRICS, 1986, 31 (03) :307-327
[6]  
Bosq D., 2000, LINEAR PROCESSES FUN, V149
[7]  
Bosq D., 1998, LECT NOTES STAT, V110
[8]   Estimating a distribution function for censored time series data [J].
Cai, ZW .
JOURNAL OF MULTIVARIATE ANALYSIS, 2001, 78 (02) :299-318
[9]   Asymptotic properties of Kaplan-Meier estimator for censored dependent data [J].
Cai, ZW .
STATISTICS & PROBABILITY LETTERS, 1998, 37 (04) :381-389
[10]  
Carbonez A., 1995, STAT DECISIONS, V44, P31