The Annals of Statistics

Bayesian Nonparametric Estimation of the Median; Part I: Computation of the Estimates

Hani Doss

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Abstract

Let $X_i, i = 1, \ldots, n$ be i.i.d. $\sim F_\theta$, where $F_\theta(x) = F(x - \theta)$ for some $F$ that has median equal to 0. $F$ is assumed unknown or only partially known, and the problem is to estimate $\theta$. Priors are put on the pair $(F, \theta)$. The priors on $F$ concentrate all their mass on c.d.f.s with median equal to 0. These priors include "Dirichlet-type" priors. The marginal posterior distribution of $\theta$ given $X_1, \ldots, X_n$ is computed. The mean of the posterior is taken as the estimate of $\theta$.

Article information

Source
Ann. Statist., Volume 13, Number 4 (1985), 1432-1444.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349746

Digital Object Identifier
doi:10.1214/aos/1176349746

Mathematical Reviews number (MathSciNet)
MR811501

Zentralblatt MATH identifier
0587.62070

JSTOR
links.jstor.org

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62G05: Estimation

Keywords
Bayes estimator Dirichlet process priors estimation of the median estimation of quantiles regular conditional distribution

Citation

Doss, Hani. Bayesian Nonparametric Estimation of the Median; Part I: Computation of the Estimates. Ann. Statist. 13 (1985), no. 4, 1432--1444. doi:10.1214/aos/1176349746. https://projecteuclid.org/euclid.aos/1176349746


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See also

  • Part II: Hani Doss. Bayesian Nonparametric Estimation of the Median; Part II: Asymptotic Properties of the Estimates. Ann. Statist., Volume 13, Number 4 (1985), 1445--1464.