Abstract
Consider a regression model in which the response is subject to random right censoring. The main goal of this paper concerns the kernel estimation of the conditional density function in the case of censored interest variable. We employ a recursive version of the Nadaraya-Watson estimator in this context. The uniform strong consistency of the recursive kernel conditional density estimator is derived. Also, we prove the asymptotic normality of this estimator.
Highlights
AMS 2000 subject classifications: 62G05, 62G07, 62G08, 62G20, 62H12
The main purpose of this paper is to study this nonparametric model when the response variable is subject to censoring, by using a kernel recursive estimation method
It dates back to [5], who introduced a class of nonparametric regression estimators for the conditional survival function in the presence of right-censoring. [8, 9] studied the asymptotic properties of the distribution and quantiles functions estimators. [17] gave a simpler proof in the randomly right-censoring case for kernel, nearest neighbor, least squares and penalized least squares estimates
Summary
Consider n pairs of independent random variables (Xi, Ti) for i = 1, . In this paper we consider the problem of nonparametric estimation of the conditional density of Y given X = x when the response variable Yi are rightly censored. The cumulative distribution function G, of the censoring random variables, is estimated by [14] estimator defined as follows n. (Xn, Yn, δn) of (X, Y, δ), the kernel estimate of the conditional density φ(t|x) denoted φn(t|x), is defined by. Where K, L are a kernels and hn is a sequence of positive real numbers. Note that this last estimator has been recently used by [15]. The Kaplan-Meir estimator is not recursive and the use of such estimator can slightly penalizes the efficiency of our estimator in term of computational time
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