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Goodness of fit tests via exponential series density estimation

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  • Marsh, Patrick

Abstract

This paper explores the properties of a new nonparametric goodness of fit test, based on the likelihood ratio test of Portnoy (1988). It is applied via the consistent series density estimator of Crain (1974) and Barron and Sheu (1991). The asymptotic properties are established as trivial corollaries to the results of those papers as well as from similar results in Marsh (2000) and Claeskens and Hjort (2004). The paper focuses on the computational and numerical properties. Specifically it is found that the choice of approximating basis is not crucial and that the choice of model dimension, through consistent selection criteria, yields a feasible procedure. Extensive numerical experiments show that the usage of asymptotic critical values is feasible in moderate sample seizes. More importantly the new tests are shown to have significantly more power than established tests such as the Kolmogorov-Smirnov, Cramer-von Mises or Anderson-Darling. Indeed, for certain interesting alternatives the power of the proposed tests may be several times that of the established ones.
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Suggested Citation

  • Marsh, Patrick, 2007. "Goodness of fit tests via exponential series density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2428-2441, February.
    • Handle: RePEc:eee:csdana:v:51:y:2007:i:5:p:2428-2441
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    1. Patrick Marsh, "undated". "Nonparametric Likelihood Ratio Tests," Discussion Papers 00/56, Department of Economics, University of York.
    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.
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    Cited by:

    1. Patrick Marsh, 2010. "A two-sample nonparametric likelihood ratio test," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 1053-1065.
    2. Patrick Marsh, 2019. "Nonparametric conditional density specification testing and quantile estimation; with application to S&P500 returns," Discussion Papers 19/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    3. 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.
    4. Patrick Marsh, 2019. "Nonparametric series density estimation and testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 77-99, March.

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