Maximal Inequalities for Degenerate $U$-Processes with Applications to Optimization Estimators
Maximal Inequalities for Degenerate $U$-Processes with Applications to Optimization Estimators
Maximal inequalities for degenerate $U$-processes of order $k, k \geq 1$, are established. The results rest on a moment inequality (due to Bonami) for $k$th-order forms and on extensions of chaining and symmetrization inequalities from the theory of empirical processes. Rates of uniform convergence are obtained. The maximal inequalities can …