Adjustments for a class of tests under nonstandard conditions

Anna Clara Monti, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    Abstract

    Generally the Likelihood Ratio statistic ? for standard hypotheses is asymptotically ?2 distributed, and the Bartlett adjustment improves the ?2 approximation to its asymptotic distribution in the sense of third-order asymptotics. However, if the parameter of interest is on the boundary of the parameter space, Self and Liang (1987) show that the limiting distribution of ? is a mixture of ?2 distributions. For such “nonstandard setting of hypotheses”, the present paper develops the third-order asymptotic theory for a class S of test statistics, which includes the Likelihood Ratio, the Wald, and the Score statistic, in the case of observations generated from a general stochastic process, providing widely applicable results. In particular, it is shown that ? is Bartlett adjustable despite its nonstandard asymptotic distribution. Although the other statistics are not Bartlett adjustable, a nonlinear adjustment is provided for them which greatly improves the ?2 approximation to their distribution and allows a subsequent Bartlett-type adjustment. Numerical studies confirm the benefits of the adjustments on the accuracy and on the power of tests whose statistics belong to S.

    Original languageEnglish
    Pages (from-to)1437-1458
    Number of pages22
    JournalStatistica Sinica
    Volume28
    Issue number3
    DOIs
    Publication statusPublished - 2018 Jul 1

    Fingerprint

    Adjustment
    Asymptotic distribution
    Test Statistic
    Power of Test
    Score Statistic
    Likelihood Ratio Statistic
    Likelihood Ratio
    Asymptotic Theory
    Approximation
    Limiting Distribution
    Parameter Space
    Stochastic Processes
    Numerical Study
    Statistics
    Class
    Test statistic
    Likelihood ratio
    Likelihood ratio statistic
    Asymptotic theory
    Nonlinear adjustment

    Keywords

    • Bartlett adjustment
    • Boundary parameter
    • High-order asymptotic theory
    • Likelihood ratio test
    • Nonstandard conditions
    • Score test
    • Wald test

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

    Cite this

    Adjustments for a class of tests under nonstandard conditions. / Monti, Anna Clara; Taniguchi, Masanobu.

    In: Statistica Sinica, Vol. 28, No. 3, 01.07.2018, p. 1437-1458.

    Research output: Contribution to journalArticle

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