The Annals of Mathematical Statistics

Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems

Monroe D. Donsker

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Abstract

Doob [1] has given heuristically an appealing methodology for deriving asymptotic theorems on the difference between the empirical distribution function calculated from a sample and the actual distribution function of the population being sampled. In particular he has applied these methods to deriving the well known theorems of Kolmogorov [2] and Smirnov [3]. In this paper we give a justification of Doob's approach to these theorems and show that the method can be extended to a wide class of such asymptotic theorems.

Article information

Source
Ann. Math. Statist. Volume 23, Number 2 (1952), 277-281.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177729445

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177729445

Mathematical Reviews number (MathSciNet)
MR47288

Zentralblatt MATH identifier
0046.35103

Citation

Donsker, Monroe D. Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems. The Annals of Mathematical Statistics 23 (1952), no. 2, 277--281. doi:10.1214/aoms/1177729445. http://projecteuclid.org/euclid.aoms/1177729445.


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