Accession Number : AD0462032

Title :   OPTIMAL ROBUSTNESS FOR ESTIMATORS AND TESTS.

Descriptive Note : Technical rept.,

Corporate Author : NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s) : Birnbaum, Allan ; Laska, Eugene

Report Date : FEB 1965

Pagination or Media Count : 55

Abstract : The present paper is intended to complement research in efficiency-robustness of estimators, by supplying formulations of concepts, techniques, and initial results for optimally efficiencyrobust estimators and tests in several types of problems. The present approach may be described as a formal indexing of alternative specifications (e.g. shapes of error-distributions) by a nuisance parameter, and adaptation of admissibility and related concepts and Bayes techniques of the Neyman-Pearson and Wald theories to the estimation and testing problems thus formulated. Specific problemsfor which new optimal efficiency-robust estimators are given are: linear estimation of location parameters; rank tests and related estimators for two-sample problems; and unbiased estimation. A by-product is a generalization of Stein's characterization of locallybest unbiased estimators to the class of admissible unbiased estimators together with the corresponding complete class theorem. (Author)

Descriptors :   (*STATISTICAL TESTS, RELIABILITY), PROBABILITY, MATHEMATICAL PREDICTION, THEOREMS, LINEAR SYSTEMS, STATISTICAL FUNCTIONS, CONVEX SETS, FUNCTIONAL ANALYSIS, SEQUENCES(MATHEMATICS), INTEGRALS, BIBLIOGRAPHIES.

Distribution Statement : APPROVED FOR PUBLIC RELEASE