Premium
Tests based on equivariant estimators
Author(s) -
Rivest LouisPaul
Publication year - 1985
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315151
Subject(s) - equivariant map , estimator , star (game theory) , mathematics , scale (ratio) , statistics , combinatorics , pure mathematics , mathematical analysis , physics , quantum mechanics
Abstract Let Ť (1) and Ť (2) be location‐equivariant estimators of an unknown location parameter μ. It is shown that the test for H 0 : μ ≤ μ 0 versus H A : μ > μ 0 that rejects H 0 if Ť (1) is large is uniformly more powerful than the one that rejects H 0 if Ť (2) is large if and only if Ť (2) is “more dispersed” than Ť (1) . A similar result is obtained for tests on scale using the star‐shaped ordering. Examples are given.