Publication details

A generalized reflection method for kernel distribution and hazard functions estimation



Year of publication 2011
Type Article in Periodical
Magazine / Source Journal of Applied Probability and Statistics
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords kernel estimation; reflection; distribution estimation
Description In this paper we focus on kernel estimates of cumulative distribution and hazard functions (rates) when the observed random variables are nonnegative. It is well known that kernel distribution estimators are not consistent when estimating a distribution function near the point x=0. This fact is rather visible in many applications, for example in kernel ROC curve estimation (Kolacek and Karunamuni (2009)). In order to avoid this problem we propose a bias reducing technique that is a kind of generalized reflection method. Our method is based on ideas of Karunamuni and Alberts (2005) and Zhang et al. (1999) developed for boundary correction in kernel density estimation. The proposed estimators are compared with the traditional kernel estimator and with the estimator based on ``classical" reflection method using simulation studies.
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