## Institute of Mathematical Statistics Lecture Notes - Monograph Series

### Sieve estimates for biased survival data

#### 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.

#### Chapter information

Source
Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, eds., Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 127-143

Dates
First available in Project Euclid: 28 November 2007

http://projecteuclid.org/euclid.lnms/1196284057

Digital Object Identifier
doi:10.1214/074921706000000644

Subjects
Primary: S62N01 62D05: Sampling theory, sample surveys
Secondary: 62G07: Density estimation

Rights