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Insensitivity of Minimax Linear Estimators
Author(s) -
Toutenburg H.
Publication year - 1983
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.19830250510
Subject(s) - minimax , estimator , mathematics , ellipsoid , minimax estimator , ridge , mile , quadratic equation , linear model , statistics , generalized linear model , mathematical optimization , minimum variance unbiased estimator , geometry , geography , geodesy , cartography
If one has prior information on the unknown parameter vector β of a linear model such that ß may be assumed to lie in a concentration ellipsoid, then the resulting minimax linear estimator (MILE) is of ridge type and has smaller quadratic risk than the GLSE. This holds whenever the prior information is a true one. The relation between MILE and GLSE is investigated under incorrect specified prior regions. The MILE is said to be robust against misspecification of the prior region, if its risk stays smaller than the risk of the GLSE.