The Annals of Statistics

Bayesian Nonparametric Estimation Based on Censored Data

Thomas S. Ferguson and Eswar G. Phadia

Full-text: Open access

Abstract

Let $X_1, \cdots, X_n$ be a random sample from an unknown $\operatorname{cdf} F$, let $y_1, \cdots, y_n$ be known real constants, and let $Z_i = \min(X_i, y_i), i = 1, \cdots, n$. It is required to estimate $F$ on the basis of the observations $Z_1, \cdots, Z_n$, when the loss is squared error. We find a Bayes estimate of $F$ when the prior distribution of $F$ is a process neutral to the right. This generalizes results of Susarla and Van Ryzin who use a Dirichlet process prior. Two types of censoring are introduced--the inclusive and exclusive types--and the class of maximum likelihood estimates which thus generalize the product limit estimate of Kaplan and Meier is exhibited. The modal estimate of $F$ for a Dirichlet process prior is found and related to work of Ramsey. In closing, an example illustrating the techniques is given.

Article information

Source
Ann. Statist., Volume 7, Number 1 (1979), 163-186.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344562

Digital Object Identifier
doi:10.1214/aos/1176344562

Mathematical Reviews number (MathSciNet)
MR515691

Zentralblatt MATH identifier
0401.62031

JSTOR
links.jstor.org

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62G05: Estimation 60K99: None of the above, but in this section

Keywords
Bayesian nonparametric estimation survival function censored data prior distribution process neutral to the right Dirichlet process processes with independent increments modal estimation

Citation

Ferguson, Thomas S.; Phadia, Eswar G. Bayesian Nonparametric Estimation Based on Censored Data. Ann. Statist. 7 (1979), no. 1, 163--186. doi:10.1214/aos/1176344562. https://projecteuclid.org/euclid.aos/1176344562


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