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VOL. 50 | 2006 Sieve estimates for biased survival data
Jiayang Sun, Bin Wang

Editor(s) Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page

## Abstract

In studies involving lifetimes, observed survival times are frequently censored and possibly subject to biased sampling. In this paper, we model survival times under biased sampling (a.k.a., biased survival data) by a semi-parametric model, in which the selection function $w(t)$ (that leads to the biased sampling) is specified up to an unknown finite dimensional parameter $\theta$, while the density function $f(t)$ of the survival times is assumed only to be smooth. Under this model, two estimators are derived to estimate the density function $f$, and a pseudo maximum likelihood estimation procedure is developed to estimate $\theta$. The identifiability of the estimation problem is discussed and the performance of the new estimators is illustrated via both simulation studies and a real data application.

## Information

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

zbMATH: 1268.62133
MathSciNet: MR2409068

Digital Object Identifier: 10.1214/074921706000000644

Subjects:
Primary: 62D05, S62N01
Secondary: 62G07

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Vol. 50 • 1 January 2006