Deconvolving Cumulative Density from Associated Random Processes

Abstract

The main purpose of the present paper is to discuss the problem of estimating the unknown cumulative density function  of  when only corrupted observations  are present, where  and  are independent unobservable random variables and  is a measurement error with a known distribution. For a sequence of strictly stationary and positively associated random variables
and assuming that the tail of the characteristic function of   behaves either as super smooth or ordinary smooth errors, we obtain the precise asymptotic expressions, the bounds on the mean-square estimation error and the asymptotic normality.