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Frequentist nonparametric goodness-of-fit tests via marginal likelihood ratios

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  • Hart, Jeffrey D.
  • Choi, Taeryon
  • Yi, Seongbaek

Abstract

A nonparametric procedure for testing the goodness of fit of a parametric density is investigated. The test statistic is the ratio of two marginal likelihoods corresponding to a kernel estimate and the parametric model. The marginal likelihood for the kernel estimate is obtained by proposing a prior for the estimate’s bandwidth, and then integrating the product of this prior and a leave-one-out kernel likelihood. Properties of the kernel-based marginal likelihood depend importantly on the kernel used. In particular, a specific, somewhat heavy-tailed, kernel K0 yields better performing marginal likelihood ratios than does the popular Gaussian kernel. Monte Carlo is used to compare the power of the new test with that of the Shapiro–Wilk test, the Kolmogorov–Smirnov test, and a recently proposed goodness-of-fit test based on empirical likelihood ratios. Properties of these tests are considered when testing the fit of normal and double exponential distributions. The new test is used to establish a claim made in the astronomy literature concerning the distribution of nebulae brightnesses in the Andromeda galaxy. Generalizations to the multivariate case are also described.

Suggested Citation

  • Hart, Jeffrey D. & Choi, Taeryon & Yi, Seongbaek, 2016. "Frequentist nonparametric goodness-of-fit tests via marginal likelihood ratios," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 120-132.
    • Handle: RePEc:eee:csdana:v:96:y:2016:i:c:p:120-132
    DOI: 10.1016/j.csda.2015.10.013
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    References listed on IDEAS

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    1. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
    2. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    3. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
    4. 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.
    5. Miecznikowski, Jeffrey & Vexler, Albert & Shepherd, Lori, 2013. "dbEmpLikeGOF: An R Package for Nonparametric Likelihood Ratio Tests for Goodness-of-Fit and Two-Sample Comparisons Based on Sample Entropy," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i03).
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