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A CLASS OF GENERALIZED BAYES MINIMAX ESTIMATORS OF A MULTIPLE REGRESSION COEFFICIENT VECTOR
Author(s) -
Lin PiErh,
Bodo Erwin P.
Publication year - 1975
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1975.tb00560.x
Subject(s) - mathematics , estimator , minimax , minimax estimator , statistics , bayes' theorem , mathematical optimization , minimum variance unbiased estimator , bayesian probability
Consider a multiple regression problem in which the dependent and (three or more) independent variables have a joint normal distribution with unknown mean vector and unknown covariance matrix. Relative to a loss function depending on the statistical design at hand, a family of minimax estimators is obtained for the regression coefficient vector. It is shown that the maximum‐likelihood estimator is dominated by the minimax estimators and hence inadmissible. A class of generalized Bayes estimators is obtained which may be expressed in terms of incomplete beta functions. With very mild conditions, the Bayes estimators are shown to be minimax.