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Stochastic compactness and point processes

Part of: Limit theorems Nonparametric inference

Published online by Cambridge University Press:  09 April 2009

L. de Hann  and
S. I. Resnick
L. de Hann
Affiliation:
Econometric Institute Erasmus UniversityRotterdam, Holland
S. I. Resnick
Affiliation:
Department of Statistics Colorado State UniversityFort Collins, Colorado 80523, U.S.A.
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Abstract

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We show that stochastic compactness of partial sums with no normal limit distribution corresponds to stochastic compactness of the point processes generated by the observations so that there exist joint limit distributions for the sample sums and the sample maxima.

MSC classification

Secondary: 60F05: Central limit and other weak theorems 62G30: Order statistics; empirical distribution functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 3 , December 1984 , pp. 307 - 316
Copyright
Copyright © Australian Mathematical Society 1984

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