A CLASS OF GENERALIZED BAYES MINIMAX ESTIMATORS OF A MULTIPLE REGRESSION COEFFICIENT VECTOR
| Autor: | Erwin P. Bodo, Pi-Erh Lin |
|---|---|
| Rok vydání: | 1975 |
| Předmět: |
Statistics and Probability
Statistics::Theory Variables Covariance matrix media_common.quotation_subject Estimator Multivariate normal distribution General Medicine Minimax Bayes' theorem Arts and Humanities (miscellaneous) Linear regression Statistics Statistics::Methodology Minimax estimator General Psychology media_common Mathematics |
| Zdroj: | British Journal of Mathematical and Statistical Psychology. 28:157-166 |
| ISSN: | 0007-1102 |
| DOI: | 10.1111/j.2044-8317.1975.tb00560.x |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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