scholarly journals Matched-Block Bootstrap for Dependent Data

Bernoulli ◽  
1998 ◽  
Vol 4 (3) ◽  
pp. 305 ◽  
Author(s):  
Edward Carlstein ◽  
Kim-Anh Do ◽  
Peter Hall ◽  
Tim Hesterberg ◽  
Hans R. Künsch ◽  
...  
2002 ◽  
Vol 18 (1) ◽  
pp. 79-98 ◽  
Author(s):  
S.N. Lahiri

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.


Biometrika ◽  
2020 ◽  
Author(s):  
T A Kuffner ◽  
S M S Lee ◽  
G A Young

Summary We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under mild strong mixing conditions. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the sub- sampling bootstrap and the moving block bootstrap, in which the number of blocks is between 1 and the ratio of sample size to block length. The hybrid block bootstrap is shown to give theoretical benefits, and startling improvements in accuracy in distribution estimation in important practical settings. The conclusion that bootstrap samples should be of smaller size than the original sample has significant implications for computational efficiency and scalability of bootstrap methodologies with dependent data. Our main theorem determines the optimal number of blocks and block length to achieve the best possible convergence rate for the block bootstrap distribution estimator for sample quantiles. We propose an intuitive method for empirical selection of the optimal number and length of blocks, and demonstrate its value in a nontrivial example.


2012 ◽  
Vol 26 (23) ◽  
pp. 3552-3560 ◽  
Author(s):  
Bihrat Önöz ◽  
Mehmetcik Bayazit

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