AN ORTHOGONAL SERIES ESTIMATOR FOR NONPARAMETRIC DENSITY ECONVOLUTION PROBLEM

Abstract

Let  be a continuous random variable with a density function  blocked and  has a compact supported   on . In this study, we examine the estimation problem  on the basis of a random sample from the distribution of random variables generated by the model . Here  is a random variable compiled with a known distribution. By applying an orthogonal series estimation method, we propose a nonparametric estimator of . We then establish some convergence results of the respective estimates against the mean integral squared error under some certain conditions set on the distributions of  and