IJPAM: Volume 5, No. 1 (2003)

A NOTE ON PARTITIONING ESTIMATE OF
CONDITIONAL DISTRIBUTION UNDER CENSORING

Ali Gannoun$^1$, Jérome Saracco$^2$, George E. Bonney$^3$
$^{1,3}$Statistical Genetics and Bioinformatics Unit
National Human Genome Center at Howard University
2216 6th Street, Suite 206
Washington D.C. 20059, USA
$^1$e-mail: gannoun@howard.edu
$^3$e-mail: ge_bonney@howard.edu
$^{1,2}$Laboratory of Probabilities and Statistics, cc 051
University of Montpellier II
34095 Montpellier Cedex 05, FRANCE
$^1$e-mail: gannoun@stat.math.univ-montp2.fr
$^2$e-mail: saracco@stat.math.univ-montp2.fr


Abstract.Let $X$ be a random variable taking values in $ {\mathbb{R}}$ and let $Y$ be a non-negative bounded random variable. Assume a right censoring random variable $C$, with continuous distribution function, operating on $Y$ such that $Y$ and $C$ are conditionally independent on given $X$. In this randomly censored situation, we want to estimate the conditional distribution of $Y$ given $X$. For this purpose, we construct a nonparametric partitioning estimate $F_{n}(y\vert x$) which is regressogram-like mean regression function estimate, and prove its uniform consistency using Dvoretzky-Kiefer-Wolfwitz $\lbrack 1\rbrack$ type inequality under censoring.

Received: February 11, 2003

AMS Subject Classification: 62N01, 62N02

Key Words and Phrases: censoring, conditional distribution, Kaplan-Meier estimator, partitioning estimate

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 1