Bayesian Nonparametric Estimation Based on Censored Data

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.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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笔记与分组

分类依据与纠错

Bayesian Nonparametric Estimation Based on Censored Data

代码、数据与补充材料

基于删失数据的贝叶斯非参数估计

原文摘要

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同方向的基础文献