The central limit theorem for empirical processes on V-Č classes: A majorizing measure approach. (English) Zbl 0833.60036
Author’s summary: K. S. Alexander [Ann. Probab. 15, 178-203 (1987; Zbl 0624.60032)] gave necessary and sufficient conditions for the central limit theorem for empirical processes on Vapnik-Červonenkis classes of functions. We present an alternative version of his result using Talagrand’s analytic characterization of pre-Gaussianness (the majorizing measure condition). Our proof can be directly extended to give the corresponding result in the non-Gaussian stable case.
Reviewer: E.Gine (College Station)
MSC:
| 60F17 | Functional limit theorems; invariance principles |
| 60B12 | Limit theorems for vector-valued random variables (infinite-dimensional case) |
Keywords:
central limit theorem for empirical processes; majorizing measures; Vapnik-Cervonenkis classesCitations:
Zbl 0624.60032References:
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