On moment-density estimation in some biased models

Abstract

This paper concerns estimating a probability density function $f$ based on iid observations from $g(x)=W^{-1}w(x)f(x)$, where the weight function $w$ and the total weight $W=\int w(x)f(x)dx$ may not be known. The length-biased and excess life distribution models are considered. The asymptotic normality and the rate of convergence in mean squared error (MSE) of the estimators are studied.

Published at http://dx.doi.org/10.1214/074921706000000536 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)