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Sudakov's typical marginals, random linear functionals and a conditional central limit theorem
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  • Published: 01 October 2002

Sudakov's typical marginals, random linear functionals and a conditional central limit theorem

  • Heinrich von Weizsäcker1 

Probability Theory and Related Fields volume 107, pages 313–324 (1997)Cite this article

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Summary.

V.N. Sudakov [Sud78] proved that the one-dimensional marginals of a high-dimensional second order measure are close to each other in most directions. Extending this and a related result in the context of projection pursuit of P. Diaconis and D. Freedman [Dia84], we give for a probability measure \(P\) and a random (a.s.) linear functional \(F\) on a Hilbert space simple sufficient conditions under which most of the one-dimensional images of \(P\) under \(F\) are close to their canonical mixture which turns out to be almost a mixed normal distribution. Using the concept of approximate conditioning we deduce a conditional central limit theorem (theorem 3) for random averages of triangular arrays of random variables which satisfy only fairly weak asymptotic orthogonality conditions.

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Authors and Affiliations

  1. Fachbereich Mathematik der Universität, Postfach 3049, D-67663 Kaiserslautern, Germany (e-mail: weizsaecker@mathematik.uni-kl.de), Kaiserslautern, Germany

    Heinrich von Weizsäcker

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  1. Heinrich von Weizsäcker
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Received: 25 July 1995 / In revised form: 20 June 1996

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von Weizsäcker, H. Sudakov's typical marginals, random linear functionals and a conditional central limit theorem. Probab Theory Relat Fields 107, 313–324 (1997). https://doi.org/10.1007/s004400050087

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  • Published: 01 October 2002

  • Issue Date: March 1997

  • DOI: https://doi.org/10.1007/s004400050087

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  • Mathematics Subject Classification: 60B11, 60F05, 28C20, 60G12
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