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January, 1975 Special Case of the Distribution of the Median
S. R. Paranjape, Herman Rubin
Ann. Statist. 3(1): 251-256 (January, 1975). DOI: 10.1214/aos/1176343016


Let $t$ be the translation parameter of a process $X(t), -\infty < t < \infty$. The likelihood ratio of the process $X(t)$ at $t$ against $t = 0$ can be written as $\exp\lbrack W(t) - \frac{1}{2}|t|\rbrack, -\infty < t < \infty$, where $W(t)$ is a standard Wiener process. For the absolute error-loss function the best invariant estimator of the translation parameter is the median of the posterior distribution. The distribution of the median for the posterior distribution is obtained, when the prior distribution for $t$ is the Lebesgue measure on the real line.


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S. R. Paranjape. Herman Rubin. "Special Case of the Distribution of the Median." Ann. Statist. 3 (1) 251 - 256, January, 1975.


Published: January, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0322.62040
MathSciNet: MR365827
Digital Object Identifier: 10.1214/aos/1176343016

Primary: 62E15
Secondary: 60G15

Keywords: Distribution of the median , Wiener process

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 1 • January, 1975
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