Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Stationary Bootstrap for U-Statistics under Strong Mixing

  • Hwang, Eunju (Department of Applied Statistics, Gachon University) ;
  • Shin, Dong Wan (Department of Statistics, Ewha Womans University)
  • Received : 2014.12.01
  • Accepted : 2014.12.27
  • Published : 2015.01.31
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Abstract

Validity of the stationary bootstrap of Politis and Romano (1994) is proved for U-statistics under strong mixing. Weak and strong consistencies are established for the stationary bootstrap of U-statistics. The theory is applied to a symmetry test which is a U-statistic regarding a kernel density estimator. The theory enables the bootstrap confidence intervals of the means of the U-statistics. A Monte-Carlo experiment for bootstrap confidence intervals confirms the asymptotic theory.

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References

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