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An Infinite Dimensional Convolution Theorem

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Statistical Decision Theory and Related Topics V

Abstract

The classical Hájek-LeCam convolution theorem assumes that the underlying parameter space is a locally compact group. Extensions to Hilbert spaces with Gaussian measures were given by Moussatat, Millar and von der Vaart. We propose an extension covering cylinder measures subject to a domination restriction on their finite dimensional projections. The proof is complex and leaves open a number of problems.

Research supported by NSF Grant DMS 9001710.

I am indebted to a referee for pointing out the works of Paterson (1983) and Wendel (1952).

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Author information

Authors and Affiliations

  1. University of California, Berkeley, USA

    L. Le Cam

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  1. L. Le Cam
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Editor information

Editors and Affiliations

  1. Department of Statistics, Purdue University, 47907, West Lafayette, IN, USA

    Shanti S. Gupta  & James O. Berger  & 

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© 1994 Springer-Verlag New York, Inc.

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Le Cam, L. (1994). An Infinite Dimensional Convolution Theorem. In: Gupta, S.S., Berger, J.O. (eds) Statistical Decision Theory and Related Topics V. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2618-5_30

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  • DOI: https://doi.org/10.1007/978-1-4612-2618-5_30

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7609-8

  • Online ISBN: 978-1-4612-2618-5

  • eBook Packages: Springer Book Archive

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