A local maximal inequality under uniform entropy |
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Authors: | van der Vaart Aad Wellner Jon A |
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Institution: | Department of Mathematics, Faculty of Sciences, Vrije Universiteit De Boelelaan 1081a, 1081 HV Amsterdam, aad@cs.vu.nl. |
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Abstract: | We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant δ. The bound is expressed in the uniform entropy integral of the class at δ. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions. |
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