Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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:

Received: 14.09.1995
Revised: 20.02.1998
Language:

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
\Bibitem{Lus98}
\by H.~Luschgy
\paper Minimaxity and equivariance in infinite dimension
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 3
\pages 540--560
\mathnet{http://mi.mathnet.ru/tvp1558}
\crossref{https://doi.org/10.4213/tvp1558}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1681068}
\zmath{https://zbmath.org/?q=an:0949.62009}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 3
\pages 388--404
\crossref{https://doi.org/10.1137/S0040585X97977045}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000085137400003}


Linking options:
  • http://mi.mathnet.ru/eng/tvp1558
  • https://doi.org/10.4213/tvp1558
  • http://mi.mathnet.ru/eng/tvp/v43/i3/p540

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:118
    Full text:31
    First page:6

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021