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Bootstrapping modified goodness-of-fit statistics with estimated parameters

Author

Listed:
  • Janssen, Paul
  • Swanepoel, Jan
  • Veraverbeke, Noël

Abstract

Goodness-of-fit tests are proposed for testing a composite null hypothesis that is a general parametric family of distribution functions. They are distribution-free under the null hypothesis and have a limiting normal distribution under the null and the alternative hypothesis. To avoid the estimation of the asymptotic variance under the alternative hypothesis, we propose consistent bootstrap estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:2:p:111-121
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    References listed on IDEAS

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    1. Too, Yeu-Hua & Lin, Gwo Dong, 1989. "Characterizations of uniform and exponential distributions," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 357-359, April.
    2. Koul, H. L. & Lahiri, S. N., 1994. "On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 255-265, May.
    3. Jiménez-Gamero, M. D. & Muñoz-García, J. & Pino-Mejías, R., 2003. "Bootstrapping parameter estimated degenerate U and V statistics," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 61-70, January.
    4. Ibrahim A. Ahmad & Ibrahim A. Alwasel, 1999. "A Goodness‐of‐fit Test for Exponentiality Based on the Memoryless Property," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 681-689.
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    Cited by:

    1. Simos Meintanis, 2008. "New inference procedures for generalized Poisson distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 751-762.
    2. Perera, Indeewara & Silvapulle, Mervyn J., 2021. "Bootstrap based probability forecasting in multiplicative error models," Journal of Econometrics, Elsevier, vol. 221(1), pages 1-24.
    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. Helena Jansen Van Rensburg & Jan Swanepoel, 2008. "A class of goodness-of-fit tests based on a new characterization of the exponential distribution," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 539-551.

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