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An unexpected property of minimax estimation in the relative squared error approach to linear regression analysis

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Abstract

An unexpected property of the relative squared error approach to linear regression analysis is derived: It is shown that an estimator being minimax among all linear affine estimators is also minimax in the set of all estimators. Two illustrative special cases are mentioned, where a generalized least squares estimator and a general ridge or Kuks-Olman estimator turn out to be minimax.

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References

  • Arnold BF, Stahlecker P (2000) Another view of the Kuks–Olman estimator. J Stat Plan Inference 89: 169–174

    Article  MathSciNet  MATH  Google Scholar 

  • Arnold BF, Stahlecker P (2002) Linear regression analysis using the relative squared error. Linear Algebra Appl 354: 3–20

    Article  MathSciNet  MATH  Google Scholar 

  • Arnold BF, Stahlecker P (2004) Some properties of the relative squared error approach to linear regression analysis. Statistics 38: 183–193

    Article  MathSciNet  MATH  Google Scholar 

  • Arnold BF, Stahlecker P (2010) A surprising property of uniformly best linear affine estimation in linear regression when prior information is fuzzy. J Stat Plan Inference 140: 954–960

    Article  MathSciNet  MATH  Google Scholar 

  • Magnus JR, Neudecker H (1988) Matrix differential calculus with applications in statistics and econometrics. Wiley, New York

    MATH  Google Scholar 

  • Pilz J (1991) Bayesian estimation and experimental design in linear regression models. Wiley, New York

    MATH  Google Scholar 

  • Rao CR, Toutenburg H (1995) Linear models, least squares and alternatives. Springer, Heidelberg

    MATH  Google Scholar 

  • Schönfeld P (2004) Least squares in general vector spaces revisited. J Econom 118: 95–109

    Article  MATH  Google Scholar 

  • Stahlecker P (1987) A priori Information und Minimax-Schätzung im linearen Regressionsmodell, Mathematical Systems in Economics, Athenäum, Frankfurt (in German)

  • Wilczyński M (2005) Minimax estimation in the linear model with a relative squared error. J Stat Plan Inference 127: 205–212

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut für Statistik und Ökonometrie, Universität Hamburg, Von-Melle-Park 5, 20146, Hamburg, Germany

    Bernhard F. Arnold & Peter Stahlecker

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  1. Bernhard F. Arnold
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  2. Peter Stahlecker
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Correspondence to Peter Stahlecker.

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Arnold, B.F., Stahlecker, P. An unexpected property of minimax estimation in the relative squared error approach to linear regression analysis. Metrika 74, 397–407 (2011). https://doi.org/10.1007/s00184-010-0309-5

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  • DOI: https://doi.org/10.1007/s00184-010-0309-5

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