Simultaneous estimation of restricted location parameters based on permutation and sign-change

Hisayuki Tsukuma ()

Statistical Papers, 2012, vol. 53, issue 4, 915-934

Abstract: The problem of simultaneously estimating location parameters is addressed, where the vector of location parameters belongs to a polyhedral cone including simple order, tree order and positive orthant restrictions and so forth. This paper proposes modified estimators based on orthogonal transformations such as sign-change and permutation and proves that, in a multivariate location family, the modified estimators are minimax under quadratic loss. Shrinkage minimax estimators improving on the modified estimators are obtained for a restricted mean vector of spherically symmetric distribution. An application of sign-change transformation is also given in estimation of a bounded normal mean. Copyright Springer-Verlag 2012

Keywords: Decision theory; Minimaxity; Order statistics; Orthogonal transformation; Restricted parameter space; Shrinkage estimator; 62H30; 62F20; 62J07 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s00362-011-0396-z

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