An Alternative Approach to Bootstrap Hypothesis Testing

Open Access
Author:
Tomlinson, Amanda S.
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
None
Committee Members:
  • Trent Gaugler, Thesis Advisor
Keywords:
  • nonparametric
  • heterogeneous
  • bootstrap
Abstract:
We propose a bootstrap procedure for hypothesis testing that avoids the conflicting nature of existing bootstrap hypothesis testing methods which employ a single observed dataset for representing the distribution of the test statistic under the null hypothesis as well as for providing evidence for rejecting the null hypothesis. Our proposed procedure, the quantile bootstrap, avoids this conflict by testing under the alternative hypothesis, which lends itself to improved power. A second level of iterations within the standard resampling scheme common to bootstrap procedures gives the procedure accurate type I error. By way of several simulations under several distributions, we show that the procedure is appropriate for many basic hypothesis tests, such as the 1-sample test of the mean, the 2-sample test of equality of means, and the test of equality of r means.