Minimax- and Gamma-minimax estimation of the bounded normal mean under LINEX-loss

Kurzfassung/Abstract

Estimating a bounded normal mean is considered under LINEX loss $$L_\alpha (\theta, d) = s \cdot \biggl( \exp \bigl\{ \alpha (d - \theta) \bigr\} - \alpha (d - \theta) - 1 \biggr),$$ where $\alpha \ne 0$ and $s > 0$ are fixed constants. It is shown that a two point prior is least favourable in case the parameter interval is small enough. So minimax and $\Gamma$-minimax estimators are determined where $\Gamma$ represents special vague prior information.