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On goodness-of-fit and the bootstrap

Author

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  • Burke, Murray D.
  • Gombay, Edit

Abstract

The empirical process, where unknown parameters of the underlying distribution function are estimated by bootstrap methods, is considered. It is approximated by a sequence of Gaussian process. In the maximum likelihood estimation case it converges to a Brownian Bridge. The asymptotic distribution of Cramer-von Mises, Anderson-Darling and Kolmogorov-Smirnov test statistics are derived.

Suggested Citation

  • Burke, Murray D. & Gombay, Edit, 1988. "On goodness-of-fit and the bootstrap," Statistics & Probability Letters, Elsevier, vol. 6(5), pages 287-293, April.
    • Handle: RePEc:eee:stapro:v:6:y:1988:i:5:p:287-293
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    Cited by:

    1. Arenal-Gutiérrez, Eusebio & Matrán, Carlos & Cuesta-Albertos, Juan A., 1996. "On the unconditional strong law of large numbers for the bootstrap mean," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 49-60, March.
    2. Csörgő, Miklós & Nasari, Masoud M., 2013. "Asymptotics of randomly weighted u- and v-statistics: Application to bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 176-192.
    3. Arenal-Gutiérrez, Eusebio & Matrán, Carlos & Cuesta-Albertos, Juan A., 1996. "Unconditional Glivenko-Cantelli-type theorems and weak laws of large numbers for bootstrap," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 365-375, March.

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