Deconvolving Cumulative Density from Associated Random Processes

Authors

  • Mohammed Es-salih Benjrada Department of Probability and Statistics, University of Sciences and Technology Houari Boumediene, Algiers, Algeria

Keywords:

Deconvolution of cumulative densities, positively associated processes, quadratic-mean convergence, asymptotic normality

Abstract

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

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Published

2022-03-28

Issue

Section

Articles