A1260
Title: Inadmissibility and transience
Authors: Kosaku Takanashi - Riken (Japan) [presenting]
Kenichiro McAlinn - Temple University (United States)
Abstract: The relation between the statistical question of inadmissibility and the probabilistic question of transience is discussed. The mathematical link between the admissibility of the mean of a Gaussian distribution and the recurrence of a Brownian motion has been proved, which holds for $\mathbb{R}^{2}$ but not for $\mathbb{R}^{3}$ in Euclidean space. This result is extended to symmetric, non-Gaussian distributions without assuming the existence of moments. As an application, it is proved that the relation between the inadmissibility of the predictive distribution of a Cauchy distribution with known scale parameter and the transience of the Cauchy process differs from dimensions $\mathbb{R}^{1}$ to $\mathbb{R}^{2}$. It is also shown that there exists an extreme model that is inadmissible in $\mathbb{R}^{1}$.
