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Estimating Quadratic Polynomials with Applications to Square Root Normalizing Transformations

In: Mathematical Statistics and Probability Theory

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  • Andrew L. Rukhin

    (University of Massachusetts, Department of Mathematics and Statistics)

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.

Suggested Citation

  • Andrew L. Rukhin, 1987. "Estimating Quadratic Polynomials with Applications to Square Root Normalizing Transformations," Springer Books, in: P. Bauer & F. Konecny & W. Wertz (ed.), Mathematical Statistics and Probability Theory, pages 205-214, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3965-3_19
    DOI: 10.1007/978-94-009-3965-3_19
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