Some inadmissibility results for estimating ordered uniform scale parameters

Abstract

Independent random samples (of possibly unequal sizes) are drawn from k (≥2) uniform populations having unknown scale parameters μ₁,…,μ_k. The problem of componentwise estimation of ordered parameters is investigated. The loss function is assumed to be squared error and the cases of known and unknown ordering among μ₁,…,μ_k. are dealt with separately. Sufficient conditions for an estimator to be inadmissible are provided and as a consequence, many natural estimators are shown to be inadmissible, Better estimators are provided.

Keywords:

• Inadmissible estimators
• Maximum likelihood estimators
• Minimum risk estimators
• Ordered parameters
• Scale parameters