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Robustness of Statistical Methods and Nonparametric Statistics pp 156–158Cite as

Minimax-Linear Estimation under Incorrect Prior Information

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Part of the book series: Theory and Decision Library ((TDLB,volume 1))

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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References

  • Kuks, J. and Olman, W. Minimaksnaja Linejnaja ozenka koeffizientow regressii. Iswestija Akademija Nauk Estonskoj SSR, 20 (1971), 480–482.

    MathSciNet  MATH  Google Scholar 

  • LÄUter, H. A minimax linear estimator for linear parameters under restrictions in form of inequalities. Math. Operationsf. Statistik 6 (1975), 689–696.

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  • Theobald, C. M. Generalizations of mean square error applied to regression. J. R. Statist. Soc, B, 36 (1974), 103–106.

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  • Toutenburg, H. Minimax-linear and MSE-estimators in generalized regression. Biometrische Zeitschrift 18 (1976) 91–100.

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  • Toutenburg, H. Prior information in linear models. John Wiley, Chichester, 1982.

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  • Yancey, T. A., Judge, G. G. and Bock, M. E. A mean square error test when stochastic restrictions are used in regression. Commun. Statist. 3 (1974), 755–768.

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Author information

Authors and Affiliations

  1. Academy of Sciences of GDR, Institute of Mathematics, Berlin, Germany

    Helge Toutenburg

Authors
  1. Helge Toutenburg
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Editor information

Editors and Affiliations

  1. Mathematical Department of Wilhelm Pieck University, Rostock, Germany

    Dieter Rasch

  2. Research Centre of Animal Production Dummerstorf-Rostock of the Academy of Agricultural Sciences of the GDR, Rostock, Germany

    Dieter Rasch

  3. Department of Statistics, McMaster University, Hamilton, Ontario, Canada

    Moti Lal Tiku

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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

  • Print ISBN: 978-94-009-6530-0

  • Online ISBN: 978-94-009-6528-7

  • eBook Packages: Springer Book Archive

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