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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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Volume 19, Issue 2

Issues

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

Walid Horrigue / Elias Ould Saïd
Published Online: 2011-04-17 | DOI: https://doi.org/10.1515/ROSE.2011.008

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

About the article

Received: 2010-10-07

Accepted: 2011-02-09

Published Online: 2011-04-17

Published in Print: 2011-06-01


Citation Information: Random Operators and Stochastic Equations, Volume 19, Issue 2, Pages 131–156, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/ROSE.2011.008.

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