Deconvolving Cumulative Density from Associated Random Processes

The main purpose of the present paper is to discuss the problem of estimating the unknown cumulative density function F(x) of X when only corrupted observations Y = X + epsilon are present, where X and epsilon are independent unobservable random variables and epsilon 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 epsilon 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.