A bias correction and acceleration approach for the problem of regions

Masao 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 - 2009 Oct 1


    • 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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