Translator Disclaimer
VOL. 49 | 2006 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 $W = \int \, w(x) \, f(x) \, d x$ 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.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62040
MathSciNet: MR2338551

Digital Object Identifier: 10.1214/074921706000000536

Subjects:
Primary: 62E99 , 62G05
Secondary: 62G20

Keywords: asymptotic normality , excess life distribution , mean squared error , moment-density estimator , Renewal process , weighted distribution