## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 23, Number 2 (1952), 169-313

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

#### 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: 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.