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Hypothesis testing and parameter estimation based onM-statistics ink samples with unequal variances
Authors:T. Shiraishi
Affiliation:(1) Department of Mathematics, Yokohama City University, 22-2, Seto, Kanazawa-ku, 236 Yokohama, Japan
Abstract:Summary Ink samples with unequal variances,M-tests for homogeneity ofk location parameters are proposed. The asymptoticχ 2-distributions of the test statistics and the robustness of the tests are investigated. NextM-estimators (ME’s) of parameters are discussed. Furthermore positive-part shrinkage versions (PSME’s) of theM-estimators for the location parameters are considered along with modified James-Stein estimation rule. In asymptotic distributional risks based on a special feasible loss, it is shown that the PSME’s dominate the ME’s, and preliminary test and shrinkageM-versions fork≧4.
Keywords:Behrens-Fisher’  s problem  robustness  asymptotic relative efficiency  asymptotic distributional risks  local alternatives  modified James-Stein rule
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