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Data Driven Likelihood Ratio Tests for Goodness-of-Fit with Estimated Parameters

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  • Patrick Marsh

Abstract

This paper generalizes the goodness of fit tests of Claeskens and Hjort (2004) and Marsh (2006) to the case where the hypothesis specifies only family of distributions. Data driven versions of these tests are based upon the Akaike and Bayesian selection criteria. The asymptotic distributions of these tests are shown to be standard, unlike those based upon the empirical distribution function. Moreover, numerical evidence suggests that under the null hypothesis performance is very similar to tests such as the Kolmogorov-Smirnov or Anderson-Darling. However, in terms of power under the alternative, the proposed tests seem to have a consistent and significant advantage.

Suggested Citation

  • Patrick Marsh, 2006. "Data Driven Likelihood Ratio Tests for Goodness-of-Fit with Estimated Parameters," Discussion Papers 06/20, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:06/20
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    References listed on IDEAS

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    1. Marsh, Patrick, 2007. "Goodness of fit tests via exponential series density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2428-2441, February.
    2. Gerda Claeskens & Nils Lid Hjort, 2004. "Goodness of Fit via Non‐parametric Likelihood Ratios," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 487-513, December.
    3. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2005. "Bootstrapping modified goodness-of-fit statistics with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 111-121, February.
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