Data driven smooth tests for composite hypotheses

Tadeusz Inglot, Wilbert C.M. Kallenberg, Teresa Ledwina

    Research output: Contribution to journalArticleAcademicpeer-review

    44 Citations (Scopus)
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    The classical problem of testing goodness-of-fit of a parametric family is reconsidered. A new test for this problem is proposed and investigated. The new test statistic is a combination of the smooth test statistic and Schwarz's selection rule. More precisely, as the sample size increases, an increasing family of exponential models describing departures from the null model is introduced and Schwarz's selection rule is presented to select among them. Schwarz's rule provides the "right" dimension given by the data, while the smooth test in the "right" dimension finishes the job. Theoretical properties of the selection rules are derived under null and alternative hypotheses. They imply consistency of data driven smooth tests for composite hypotheses at essentially any alternative.
    Original languageEnglish
    Pages (from-to)1222-1250
    Number of pages29
    JournalAnnals of statistics
    Issue number3
    Publication statusPublished - 1997


    • Goodness of Fit
    • Schwarz's BIC criterion
    • Neyman's test
    • data driven procedure
    • MSC-62G10
    • MSC-62G20
    • Smooth test

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