### Abstract

For location families with densities f_{0}(x - θ), we study the problem of estimating θ for location invariant loss L(θ, d) = ρ(d - θ), and under a lower-bound constraint of the form θ ≥ a. We show, that for quite general (f_{0}, ρ), the Bayes estimator δ_{U} with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous dominance results due to Katz and Farrell, we make use of Kubokawa's IERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and are characterized in terms of δ_{U}. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint of the form θ ∈ [a, b].

Original language | English (US) |
---|---|

Pages (from-to) | 129-143 |

Number of pages | 15 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2005 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Keywords

- Constrained parameter space
- Dominating estimators
- Location family
- Lower-bounded parameter
- Minimax estimation
- Minimum risk equivariant estimator