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Bootstrapping convex hulls

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  • Zarepour, M.
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    Abstract

    If the distribution of observations satisfies a multivariate regular variation condition then the asymptotic distribution of convex hulls can be modeled by using point processes. The limiting distributions cannot be simplified and are extremely difficult to use. We show the bootstrap is asymptotically valid if the resampling sample size is m=o(n), where n is the original sample size. We use this to also provide an asymptotically valid bootstrap for the area and perimeter of the convex hulls. Also, under a circularly symmetric distribution an alternative and consistent Monte Carlo method is studied.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-3XVPF3P-7/2/d0dd875b7ba1513359c3654243b244e1
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 45 (1999)
    Issue (Month): 1 (October)
    Pages: 55-63

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    Handle: RePEc:eee:stapro:v:45:y:1999:i:1:p:55-63

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    Related research

    Keywords: Convex hull Bootstrap Point process Monte Carlo Asymptotic;

    References

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    1. Lepage, Raoul & Podg├│rski, Krzysztof, 1996. "Resampling Permutations in Regression without Second Moments," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 119-141, April.
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    Cited by:
    1. Zarepour, M. & Knight, K., 1999. "Bootstrapping point processes with some applications," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 81-90, November.

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