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October, 1987 Donsker Classes and Random Geometry
Michel Talagrand
Ann. Probab. 15(4): 1327-1338 (October, 1987). DOI: 10.1214/aop/1176991979


Let $\mathscr{F}$ be a class of square integrable functions. We give necessary and sufficient random geometric conditions for the empirical process indexed by $\mathscr{F}$ to satisfy the CLT. These conditions roughly mean that the trace of $\mathscr{F}$ on a random sample is a small (for the $l^1$ norm) perturbation of a set which is nice for the $l^2$ norm.


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Michel Talagrand. "Donsker Classes and Random Geometry." Ann. Probab. 15 (4) 1327 - 1338, October, 1987.


Published: October, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0637.60040
MathSciNet: MR905334
Digital Object Identifier: 10.1214/aop/1176991979

Primary: 60F17
Secondary: 60B12 , 60F05 , 62E20

Keywords: central limit theorems , Empirical processes , functional Donsker classes , Metric entropy

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 4 • October, 1987
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