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Estimating Quadratic Polynomials with Applications to Square Root Normalizing Transformations

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Mathematical Statistics and Probability Theory

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Abstract

Assume that the observed sample y1…,yn is approximately normalized by the square root transformation, x = 2(y1/2)-1) which belongs to the Box-Cox family of normalizing transformations. The unknown mean of the original y’s sample is a quadratic function of the normal parameters of the transformed sample We study the behavior of a natural estimator of this and more general quadratic functions of normal parameters and obtain a necessary and sufficient condition for its admissibility under quadratic loss. In the case of inadmissibility, a class of better estimators is exhibited.

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Referneces

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    Andrew L. Rukhin

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  1. Andrew L. Rukhin
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Editor information

Editors and Affiliations

  1. University of Cologne, Germany

    P. Bauer

  2. University of Agriculture, Vienna, Austria

    F. Konecny

  3. Technical University, Vienna, Austria

    W. Wertz

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© 1987 by D. Reidel Publishing Company, Dordrecht, Holland

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Rukhin, A.L. (1987). Estimating Quadratic Polynomials with Applications to Square Root Normalizing Transformations. In: Bauer, P., Konecny, F., Wertz, W. (eds) Mathematical Statistics and Probability Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3965-3_19

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  • DOI: https://doi.org/10.1007/978-94-009-3965-3_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8259-4

  • Online ISBN: 978-94-009-3965-3

  • eBook Packages: Springer Book Archive

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