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Integrated squared error of kernel-type estimator of distribution function
Authors:Shingo Shirahata  In-Sun Chu
Affiliation:(1) Department of Statistics, School of General Education, Osaka University, 560 Toyonaka, Osaka, Japan;(2) Department of Mathematical Science, Faculty of Engineering Science, Osaka University, 560 Toyonaka, Osaka, Japan
Abstract:Let X1,...,Xn be a random sample drawn from distribution function F(x) with density function f(x) and suppose we want to estimate X(x). It is already shown that kernel estimator of F(x) is better than usual empirical distribution function in the sense of mean integrated squared error. In this paper we derive integrated squared error of kernel estimator and compare the error with that of the empirical distribution function. It is shown that the superiority of kernel estimators is not necessarily true in the sense of integrated squared error.
Keywords:Nonparametric distribution function estimator  kernel function  mean integrated squared error  integrated squared error
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