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Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems
Open accessAbstract
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.
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Cited by
Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
Anderson, T. W., & Darling, D. A. (1952) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729437 · Cited by 3,542
Dvoretzky, A., Kiefer, J., & Wolfowitz, J. (1956) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728174 · Cited by 964
Probability: Theory and Examples
Durrett, R. (2019) · doi:10.1017/9781108591034 · Cited by 857
Metadata
- Authors
- Donsker, M. D.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1952-06
- Volume
- 23
- Issue
- 2
- Pages
- 277-281
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2010731048
- Cited by
- 320
- References
- 0
- FWCI
- 2.82
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Donsker, M. D. (1952). Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems. The Annals of Mathematical Statistics. https://doi.org/10.1214/aoms/1177729445
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