Abstract
If nonlinear prior information on the parameter β of the familiar linear regression model is available such that β may be assumed to be in a convex set (a concentration ellipsoid), then this information is used optimally by a minimax estimator (MILE). The MILE is of ridge type and is of smaller minimax risk compared with the BLUE so far the prior information is true. The MILE is said to be insensitive against misspecifications of the prior region if its risk stays smaller than the risk of the BLUE. There are given necessary and sufficient conditions for the insensitivity of MILE in typical situations of incorrect prior information.
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© 1984 Academy of Agricultural Sciences of the GDR, Research Centre of Animal Production, Dummerstorf-Rostock, DDR 2551 Dummerstorf.
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Toutenburg, H. (1984). Minimax-Linear Estimation under Incorrect Prior Information. In: Rasch, D., Tiku, M.L. (eds) Robustness of Statistical Methods and Nonparametric Statistics. Theory and Decision Library, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6528-7_35
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DOI: https://doi.org/10.1007/978-94-009-6528-7_35
Publisher Name: Springer, Dordrecht
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