BOUNDING THE EXPECTATION OF THE SUPREMUM OF AN EMPIRICAL PROCESS OVER A (WEAK) VC-MAJOR CLASS

Yannick Baraud (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

Given a bounded class of functions G and independent random variables X1, . . . , Xn, we provide an upper bound for the expectation of the supremum of the empirical process over elements of G having a small variance. Our bound applies in the cases where G is a VC-subgraph or a VC-major class and it is of smaller order than those one could get by using a universal entropy bound over the whole class G . It also involves explicit constants and does not require the knowledge of the entropy of G

Domaines: Probabilités [math.PR]

Yannick Baraud. BOUNDING THE EXPECTATION OF THE SUPREMUM OF AN EMPIRICAL PROCESS OVER A (WEAK) VC-MAJOR CLASS. Electronic Journal of Statistics , 2016, 11. ⟨hal-01085004v2⟩