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Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors
-
Walid Horrigue
and
Elias Ould Saïd
Published/Copyright:
April 17, 2011
Abstract
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.
Keywords.: Censored data; conditional distribution function; infinite dimension; Kaplan–Meier estimator; kernel estimator; small-ball probability
Received: 2010-10-07
Accepted: 2011-02-09
Published Online: 2011-04-17
Published in Print: 2011-June
© de Gruyter 2011
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Keywords for this article
Censored data;
conditional distribution function;
infinite dimension;
Kaplan–Meier estimator;
kernel estimator;
small-ball probability
Articles in the same Issue
- To Anatolii Volodymyrovych Skorokhod's memory
- Preface
- Almost sure asymptotic stability and convergence of stochastic Theta methods applied to systems of linear SDEs in
- Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors
- Central limit theorem associated with bilinear random fields
- Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations
- An improvement of subword complexity
- Estimation of the long memory parameter in stochastic volatility models by quadratic variations
