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
Rights: Copyright © 2006, Institute of Mathematical Statistics
