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Joshua Arfin - A Monte Carlo Investigation of the Bootstrap for U-Statistics

Presented by:
Joshua Arfin
Abstract:

U-statistics are a useful class of statistics that arise in many common situations (e.g. sample means and variances) and about which much is known. In many cases, the asymptotic distributions of U-statistics are simple, but in others, they are much more complex, and in some cases, intractable. In these more complicated scenarios, when one wants to use the statistics in practice and needs to understand their probability distribution (for inferential reasons, for example), one must approximate the distribution via some computational approach. The most prominent such approach of the last 30 years has been the bootstrap, though bootstrap methods for U-statistics remain underdeveloped. In this research we explore the choice of the distribution of the weights for the stochastically reweighted bootstrap. We present the results of simulation studies to assess the level and power of tests based on this bootstrap scheme under a variety of conditions.