The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 23, Number 2 (1952), 277-281.
Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems
Doob  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  and Smirnov . 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.
Ann. Math. Statist. Volume 23, Number 2 (1952), 277-281.
First available in Project Euclid: 28 April 2007
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Donsker, Monroe D. Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems. Ann. Math. Statist. 23 (1952), no. 2, 277--281. doi:10.1214/aoms/1177729445. https://projecteuclid.org/euclid.aoms/1177729445