Strong approximations for the general bootstrap of empirical processes with applications in selected topics of nonparametric statistics

S. Bouzebda and O. El-Dakkak

The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in [40]. The proof is based on the same arguments used in [37]. As a consequence, we establish an approximation of the bootstrapped kernel distribution estimation. Furthermore, our results are applied to two-sample testing procedures as well as to change-point problems. We end with establishing strong approximations of the bootstrapped empirical process when the parameters are estimated.

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