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http://dx.doi.org/10.5351/CSAM.2015.22.1.081

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)
Publication Information
Communications for Statistical Applications and Methods / v.22, no.1, 2015 , pp. 81-93 More about this Journal
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.
Keywords
Stationary bootstrap; U-statistic; strong mixing; strong consistency; weak consistency; Monte Carlo study;
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