Open AccessBAYESIAN ESTIMATORS, ROBUST ESTIMATORS: A COMPARISON AND SOME ASYMPTOTIC RESULTS
Author(s) -
Jones Douglas H.
Publication year - 1984
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2330-8516.1984.tb00082.x
Subject(s) - estimator , bayes' theorem , mathematics , bayesian probability , extremum estimator , bayes estimator , m estimator , bootstrapping (finance) , scale (ratio) , statistics , econometrics , physics , quantum mechanics
Combinations of Bayes and resistant estimators of latent ability were studied in Wainer and Thissen (1984), who show that they have desirable performances for small to medium samples especially in the presence of contamination. While their study was based on computer simulations, this note provides the first order asymptotic theory, from which one may compute approximations to the standard errors of the estimators. A side issue concerns the “overshrinking phenomenon” which caused Wainer and Thissen to expand the scale of the estimators in order to increase their accuracy and to make them more comparable to the traditional estimators. This note derives a differential equation specifying a transform that may make Bayes/resistant estimators even more favorable.