Bootstrap-Based Hypothesis Testing

Master thesis (2023)

Authors

M. Galanis Electrical Engineering, Mathematics and Computer Science

Contributors

Alexis Derumigny Statistics - EEMCS (mentor)
Gianluca Finocchio University of Vienna (graduation committee member)
A.W. van der Vaart Statistics - EEMCS (graduation committee member)
D. Kurowicka Applied Probability - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Miltos Galanis
More Info
expand_more

Published Date

26-10-2023

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this thesis, we explore the structure of consistent bootstrap statistics in hypothesis testing. Bootstrap, as a very useful technique when theoretical distributions are not available or when the sample size is small, enjoys a lot of interest from applied statisticians. Historically, guidelines for performing Bootstrap have been proposed. One of the guidelines proposed is to center the bootstrap statistic around the true statistic, calculated from the original sample. The second, is to perform resampling in a way such that the new sample reflects the hypothesis tested. However, both of the guidelines are proposed based mostly on an empirical point of view. In this project, we show that the calculation of the bootstrap statistic is directly related to the way the new sample is generated. We describe the specific conditions under which the Bootstrap statistic should or should not be centered around the true. As mentioned the resampling scheme that is picked directly influences this choice. The motivation is derived from the independence test and the same arguments apply to the regression slope test. Finally, we provide a generalized setting where a consistent bootstrap statistic is provided, based on the resampling scheme that is picked.