Consistency and Monte Carlo Simulation of a Data Driven Version of smooth Goodness-of-Fit Tests

Wilbert C.M. Kallenberg, Teresa Ledwina

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    Abstract

    The data driven method of selecting the number of components in Neyman's smooth test for uniformity, introduced by Ledwina, is extended. The resulting tests consist of a combination of Schwarz's Bayesian information criterion (BIC) procedure and smooth tests. The upper bound of the dimension of the exponential families in applying Schwarz's rule is allowed to grow with the number of observations to infinity. Simulation results show that the data driven version of Neyman's test performs very well for a wide range of alternatives and is competitive with other recently introduced (data driven) procedures. It is shown that the data driven smooth tests are consistent against essentially all alternatives. In proving consistency, new results on Schwarz's selection rule are derived, which may be of independent interest.
    Original languageEnglish
    Pages (from-to)1594-1608
    Number of pages15
    JournalAnnals of statistics
    Volume23
    Issue number5
    DOIs
    Publication statusPublished - 1995

    Keywords

    • Neyman's test
    • exponential family
    • smooth test
    • METIS-140696
    • Monte Carlo power
    • Goodness of Fit
    • Schwarz's BIC criterion
    • IR-70371

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