### 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) |
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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 |

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### 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

### Cite this

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**Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval.** / Marchand, Éric; Strawderman, William.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval

AU - Marchand, Éric

AU - Strawderman, William

PY - 2005/1/1

Y1 - 2005/1/1

N2 - For location families with densities f0(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 (f0, ρ), the Bayes estimator δU 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 δU. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint of the form θ ∈ [a, b].

AB - For location families with densities f0(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 (f0, ρ), the Bayes estimator δU 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 δU. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint of the form θ ∈ [a, b].

KW - Constrained parameter space

KW - Dominating estimators

KW - Location family

KW - Lower-bounded parameter

KW - Minimax estimation

KW - Minimum risk equivariant estimator

UR - http://www.scopus.com/inward/record.url?scp=23744472821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23744472821&partnerID=8YFLogxK

U2 - 10.1007/BF02506883

DO - 10.1007/BF02506883

M3 - Article

AN - SCOPUS:23744472821

VL - 57

SP - 129

EP - 143

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 1

ER -