Data-driven smooth tests when the hypothesis Is composite

Wilbert C.M. Kallenberg, Teresa Ledwina

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    In recent years several authors have recommended smooth tests for testing goodness of fit. However, the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur. Schwarz's selection rule provides one such good choice. Earlier results on simple null hypotheses are extended here to composite hypotheses, which tend to be of more practical interest. For general composite hypotheses, consistency of the data-driven smooth tests holds at essentially any alternative. Monte Carlo experiments on testing exponentiality and normality show that the data-driven version of Neyman's test compares well to other, even specialized, tests over a wide range of alternatives.
    Original languageEnglish
    Pages (from-to)1094-1104
    Number of pages11
    JournalJournal of the American Statistical Association
    Issue number439
    Publication statusPublished - 1997


    • Neyman's test
    • Goodness of Fit
    • Schwarz's BIC criterion
    • Monte Carlo study


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