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July 1996 On the convergence of scaled random samples
Geoffrey Pritchard
Ann. Probab. 24(3): 1490-1506 (July 1996). DOI: 10.1214/aop/1065725190

Abstract

The scaled-sample problem asks the following question: given a distribution on a normed linear space E, when do there exist constants ${\gamma_n} such that $X^{(j)}/\gamma_n}_{j=1}^n$ converges as $n \to \infty$ (in the Hausdorff metric given by the norm) to a fixed set K? (Here ${X^{(j)}}$ are i.i.d. with the given distribution). The main result presented here relates the convergence of scaled samples to a large deviation principle for single observations, thereby achieving a dimension-free description of the problem.

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Geoffrey Pritchard. "On the convergence of scaled random samples." Ann. Probab. 24 (3) 1490 - 1506, July 1996. https://doi.org/10.1214/aop/1065725190

Information

Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0870.60047
MathSciNet: MR1411503
Digital Object Identifier: 10.1214/aop/1065725190

Subjects:
Primary: 60B12, 60G70
Secondary: 60B11, 60D05, 60F15

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 3 • July 1996
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