Summary
Alexander (1987) gave necessary and sufficient conditions for the central limit theorem for empirical processes on Vapnik-Červonenkis classes of functions. In this paper we present an alternative version of his result using Talagrand’s analytic characterization of pregaussianness (the majorizing measure condition). Our proof can be directly extended to give the corresponding result in the non-gaussian stable case.
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Romo, J. The central limit theorem for empirical processes on V-Č classes: A majorizing measure approach. Test 3, 47–72 (1994). https://doi.org/10.1007/BF02562693
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DOI: https://doi.org/10.1007/BF02562693