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 Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 3, Pages 540–560 (Mi tvp1558)

Minimaxity and equivariance in infinite dimension

H. Luschgy

Department IV, Mathematics, University of Trier, Germany

Abstract: In a location model on an infinite-dimensional Banach space, we study the problem of estimating the location parameter. This estimation problem exhibits an invariance structure where the group involved is the Banach space itself. Under suitable conditions it is shown that the minimax risk coincides with the minimum risk over all equivariant estimators, thus establishing the minimaxity of minimum risk equivariant estimators. Furthermore, such estimators are shown to be extended Bayes estimators, and least favorable sequences of prior distributions are derived. The proofs rely on a general result for structure models and a concentration condition for probability measures on a Banach space related to reproducing kernel Hilbert spaces of Gaussian measures.

Keywords: infinite-dimensional location model, structure model, equivariant estimator, minimax estimator, shift group.

DOI: https://doi.org/10.4213/tvp1558

Full text: PDF file (1117 kB)

English version:
Theory of Probability and its Applications, 1999, 43:3, 388–404

Bibliographic databases:

Revised: 20.02.1998
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Citation: H. Luschgy, “Minimaxity and equivariance in infinite dimension”, Teor. Veroyatnost. i Primenen., 43:3 (1998), 540–560; Theory Probab. Appl., 43:3 (1999), 388–404

Citation in format AMSBIB
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