Bounding the resampling risk for sequential Monte Carlo implementation of hypothesis tests

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6 Scopus citations

Abstract

Sequential designs can be used to save computation time in implementing Monte Carlo hypothesis tests. The motivation is to stop resampling if the early resamples provide enough information on the significance of the p-value of the original Monte Carlo test. In this paper, we consider a sequential design called the B-value design proposed by Lan and Wittes and construct the sequential design bounding the resampling risk, the probability that the accept/reject decision is different from the decision from complete enumeration. For the B-value design whose exact implementation can be done by using the algorithm proposed in Fay, Kim and Hachey, we first compare the expected resample size for different designs with comparable resampling risk. We show that the B-value design has considerable savings in expected resample size compared to a fixed resample or simple curtailed design, and comparable expected resample size to the iterative push out design of Fay and Follmann. The B-value design is more practical than the iterative push out design in that it is tractable even for small values of resampling risk, which was a challenge with the iterative push out design. We also propose an approximate B-value design that can be constructed without using a specially developed software and provides analytic insights on the choice of parameter values in constructing the exact B-value design.

Original languageEnglish (US)
Pages (from-to)1834-1843
Number of pages10
JournalJournal of Statistical Planning and Inference
Volume140
Issue number7
DOIs
StatePublished - Jul 1 2010

Keywords

  • Approximation
  • B-value
  • Bootstrap
  • Permutation
  • Sequential design

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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