The Annals of Statistics

Bayesian Nonparametric Estimation Based on Censored Data

Thomas S. Ferguson and Eswar G. Phadia

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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.

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

First available in Project Euclid: 12 April 2007

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

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


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.

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