# Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications

@article{Chen2019JackknifeMB, title={Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications}, author={Xiaohui Chen and Kengo Kato}, journal={Probability Theory and Related Fields}, year={2019} }

This paper is concerned with finite sample approximations to the supremum of a non-degenerate $U$-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the $U$-process itself is not weakly convergent as a process. Such situations arise in a variety of modern statistical problems. We first consider Gaussian approximations, namely, approximate the $U…

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