ON THE JACKKNIFE-AFTER-BOOTSTRAP METHOD FOR DEPENDENT DATA AND ITS CONSISTENCY PROPERTIES
针对相依数据，提出一种移动块刀切法来估计块自助估计量的标准误，并证明该估计量对一大类统计量的偏差和方差估计具有一致性。
Motivated by Efron (1992, Journal of the Royal Statistical Society, Series B 54, 83–111), 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.