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Bootstrapping parameter estimated degenerate U and V statistics

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  • Jiménez-Gamero, M. D.
  • Muñoz-García, J.
  • Pino-Mejías, R.

Abstract

Let X1,X2,...,Xn be independent random vectors with common distribution function F and let be a parametric family of distributions. Let Tn([theta])=Tn(X1,X2,...,Xn;[theta]) be a degree-2 V statistic and let be a consistent estimator of [theta]. Several test statistics for testing the composite null hypothesis has the form . Typically, the null distribution of depends on the unknown value of [theta]. The purpose of this paper is to show that the bootstrap can be used to approximate the null distribution of this type of statistics. We also give similar results for statistics , with Wn([theta]) a degree-2 U statistic.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:1:p:61-70
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    References listed on IDEAS

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    1. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
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    Cited by:

    1. 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.
    2. Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.

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