Estimating Quadratic Polynomials with Applications to Square Root Normalizing Transformations

Andrew L. Rukhin
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Andrew L. Rukhin: University of Massachusetts, Department of Mathematics and Statistics

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 205-214 from Springer

Abstract: 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.

Keywords: Quadratic Polynomial; Prior Density; Quadratic Loss; Shrinkage Estimator; Maximum Likelihood Estima (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3965-3_19

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DOI: 10.1007/978-94-009-3965-3_19

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