A unified minimax result for restricted parameter spaces

TL;DR

This paper unifies and extends minimax results across various restricted parameter estimation problems, simplifying the theoretical framework and broadening applicability in statistical inference.

Contribution

It provides a comprehensive unification and extension of minimax results for a wide range of restricted parameter estimation problems.

Findings

Unified framework for minimax estimation in restricted spaces

Extended applicability to various parameter restrictions

Simplified derivation of minimax results

Abstract

We provide a development that unifies, simplifies and extends considerably a number of minimax results in the restricted parameter space literature. Various applications follow, such as that of estimating location or scale parameters under a lower (or upper) bound restriction, location parameter vectors restricted to a polyhedral cone, scale parameters subject to restricted ratios or products, linear combinations of restricted location parameters, location parameters bounded to an interval with unknown scale, quantiles for location-scale families with parametric restrictions and restricted covariance matrices.