Rates of growth and sample moduli for weighted empirical processes indexed by sets
Probability inequalities are obtained for the supremum of a weighted empirical process indexed by a Vapnik-Červonenkis class \({\mathbb{C}}\) of sets. These inequalities are particularly useful under the assumption \[ P(\cup \{C\in {\mathbb{C}}:\quad P(C)<t\})\to 0\quad as\quad t\to 0. \] They are used to obtain almost sure bounds on the rate of growth of the process as the sample size approaches infinity, to find an asymptotic sample modulus for the unweighted empirical process, and to study the ratio \(P_ n/P\) of the empirical measure to the actual measure.
supremum of a weighted empirical process
scientific article; zbMATH DE number 3960661
scientific article