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Distribution free testing of goodness of fit in a one dimensional parameter space

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  • Roberts, Leigh A.

Abstract

We propose two versions of asymptotically distribution free empirical processes. When a composite null hypothesis contains a family of distributions indexed by a one dimensional parameter space, and when that single parameter is estimated by maximum likelihood, the resulting distribution free goodness of fit tests are simpler than tests applying the Khmaladze transformation. For the Pareto distribution, the process we advocate is especially simple. The theory is illustrated by fitting the Pareto distribution to threshold exceedances of stock returns, and the Weibull distribution to fibre strength data.

Suggested Citation

  • Roberts, Leigh A., 2015. "Distribution free testing of goodness of fit in a one dimensional parameter space," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 215-222.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:215-222
    DOI: 10.1016/j.spl.2015.01.002
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    References listed on IDEAS

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    1. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    2. Vo, Long H. & Roberts, Leigh, 2014. "On long memory behaviour and predictability of financial markets," Working Paper Series 3361, Victoria University of Wellington, School of Economics and Finance.
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    Cited by:

    1. González-Estrada, Elizabeth & Villaseñor, José A., 2016. "A ratio goodness-of-fit test for the Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 30-35.

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