Maximal Inequalities for Degenerate U-processes with Applications to Optimization Estimators
نویسنده
چکیده
Maximal Inequalities for degenerate U-processes of order k, k ≥ 1, are established. The results rest on a moment inequality (due to Bonami (1970)) for kth-order forms, and extensions of chaining and symmetrization inequalities from the theory of empirical processes. Rates of uniform convergence are obtained. The maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having U-process structure. As an application, a semiparametric regression estimator that maximizes a U-process of order three is shown to be √ n-consistent and asymptotically normally distributed.
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