Year: 1975
Type: article
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.
Source: The Annals of Statistics
Authors: S. R. Paranjape, Herman Rubin
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2057366196