Tests for monotonicity of a regression mean with guaranteed level

Irène Gijbels, Peter Hall, M. C. Jones, Inge Koch

    Research output: Contribution to journalArticle

    27 Citations (Scopus)

    Abstract

    In this paper a nonparametric procedure for testing for monotonicity of a regression mean with guaranteed level is proposed. The procedure is based on signs of differences of observations from the response variable. The test is calibrated against the most difficult null hypothesis, when the regression function is constant, and produces an exact test in this context. In general, the test is conservative. The power of the test is good, and comparable with that of other nonparametric tests. It is shown that the testing procedure has asymptotic power 1 against certain local alternatives. The method is also robust against heavy-tailed error distributions, and even maintains good power when the errors are for example Cauchy distributed. A simulation study is provided to demonstrate finite-sample behaviour of the testing procedure.

    Original languageEnglish
    Pages (from-to)663-673
    Number of pages11
    JournalBiometrika
    Volume87
    Issue number3
    DOIs
    Publication statusPublished - 1 Jan 2000

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