A bias correction and acceleration approach for the problem of regions

M. Ueki, K. Fueda

Research output: Contribution to journalArticlepeer-review


For testing the problem of regions in the space of distribution functions, this paper considers approaches to modify the bootstrap probability to be a second-order accurate p-value based on the familiar bias correction and acceleration method. It is shown that Shimodaira's [2004a. Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling. Ann. Statist. 32, 2616-2641] twostep-multiscale bootstrap method works even in the problem of regions in functional space. In this paper the bias correction quantity is estimated by his onestep-multiscale bootstrap method. Instead of using the twostep-multiscale bootstrap method, the acceleration constant is estimated by a newly proposed jackknife method which requires first-level bootstrap resamplings only. Some numerical examples are illustrated, in which an application to testing significance in model selection is included.

Original languageEnglish
Pages (from-to)3533-3542
Number of pages10
JournalJournal of Statistical Planning and Inference
Issue number10
Publication statusPublished - Oct 1 2009


  • Bias correction and acceleration
  • Edgeworth expansion
  • Jackknife method
  • Multiscale-multistep bootstrap method
  • Problem of regions
  • Second-order unbiased p-value
  • Significance of model selection

ASJC Scopus subject areas

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


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