A local maximal inequality under uniform entropy

作者：van der Vaart Aad^*; Wellner Jon A

来源：Electronic Journal of Statistics, 2011, 5: 192-203.

DOI：10.1214/11-EJS605

• Empirical process
• modulus of continuity
• minimum contrast estimator
• rate of convergence

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 delta. The bound is expressed in the uniform entropy integral of the class at delta. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions.

• 出版日期2011