ON THE JACKKNIFE-AFTER-BOOTSTRAP METHOD FOR DEPENDENT DATA AND ITS CONSISTENCY PROPERTIES
Econometric Theory, 2002, vol. 18, issue 1, 79-98
Motivated by Efron (1992, Journal of the Royal Statistical Society, Series B 54, 83â€“111), this paper proposes a version of the moving block jackknife as a method of estimating standard errors of block-bootstrap estimators under dependence. As in the case of independent and identically distributed (i.i.d.) observations, the proposed method merely regroups the values of a statistic from different bootstrap replicates to produce an estimate of its standard error. Consistency of the resulting jackknife standard error estimator is proved for block-bootstrap estimators of the bias and the variance of a large class of statistics. Consistency of Efron's method is also established in similar problems for i.i.d. data.
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