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Beyond the heuristic approach to Kolmogorov-Smirnov theorems

Published online by Cambridge University Press:  14 July 2016

David Pollard
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Abstract

The theory of weak convergence has developed into an extensive and useful, but technical, subject. One of its most important applications is in the study of empirical distribution functions: the explication of the asymptotic behavior of the Kolmogorov goodness-of-fit statistic is one of its greatest successes. In this article a simple method for understanding this aspect of the subject is sketched. The starting point is Doob's heuristic approach to the Kolmogorov-Smirnov theorems, and the rigorous justification of that approach offered by Donsker. The ideas can be carried over to other applications of weak convergence theory.

Keywords

WEAK CONVERGENCEKOLMOGOROV STATISTICDOOB'S HEURISTIC APPROACHDONSKER'S THEOREMUNIFORM TOPOLOGY ON D[0, 1]POISSONIZATION
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 359 - 365
Copyright
Copyright © 1982 Applied Probability Trust 

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