## The Annals of Statistics

### Special Case of the Distribution of the Median

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 3, Number 1 (1975), 251-256.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343016

Digital Object Identifier
doi:10.1214/aos/1176343016

Mathematical Reviews number (MathSciNet)
MR365827

Zentralblatt MATH identifier
0322.62040

JSTOR