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December, 1985 Bayesian Nonparametric Estimation of the Median; Part II: Asymptotic Properties of the Estimates
Hani Doss
Ann. Statist. 13(4): 1445-1464 (December, 1985). DOI: 10.1214/aos/1176349747

Abstract

For data $\theta + \varepsilon_i, i = 1, \ldots, n$ where $\varepsilon_i$ are i.i.d. $\sim F$ with the median of $F$ equal to $0$ but $F$ otherwise unknown, it is desired to estimate $\theta$. In Doss (1985) priors are put on the pair $(F, \theta)$, the marginal posterior distribution of $\theta$ is computed, and the mean of the posterior is taken as the estimate of $\theta$. In the present paper a frequentist point of view is adopted. The consistency properties of the Bayes estimates computed in Doss (1985) are investigated when the prior on $F$ is of the "Dirichlet-type." Any $F$ whose median is 0 is in the support of these priors. It is shown that if the $\varepsilon_i$ are i.i.d. from a discrete distribution, then the Bayes estimates are consistent. However, if the distribution of the $\varepsilon_is$ is continuous, the Bayes estimates can be inconsistent.

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Hani Doss. "Bayesian Nonparametric Estimation of the Median; Part II: Asymptotic Properties of the Estimates." Ann. Statist. 13 (4) 1445 - 1464, December, 1985. https://doi.org/10.1214/aos/1176349747

Information

Published: December, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0587.62071
MathSciNet: MR811502
Digital Object Identifier: 10.1214/aos/1176349747

Subjects:
Primary: 62A15
Secondary: 62G05

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 4 • December, 1985
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