Bootstrap-Based Hypothesis Testing

Bootstrap-Based Hypothesis Testing

Galanis, Miltos (TU Delft Electrical Engineering, Mathematics and Computer Science)

Derumigny, Alexis (mentor)
Finocchio, Gianluca (graduation committee)
van der Vaart, A.W. (graduation committee)
Kurowicka, D. (graduation committee)

Delft University of Technology

Applied Mathematics

2023-10-26

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.

statistics
bootstrap
hypothesis
testing
empirical processes
weak convergence

http://resolver.tudelft.nl/uuid:e90f29d0-a855-471e-9352-a9777e3cbd4d

Student theses

master thesis

© 2023 Miltos Galanis