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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.
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This content will become publicly available on December 1, 2025
Prepivoted Augmented Dickey-Fuller Test with Bootstrap-Assisted Lag Length Selection
We investigate the application of prepivoting in conjunction with lag length selection to correct the size and power performance of the Augmented Dickey-Fuller test for a unit root. The bootstrap methodology used to perform the prepivoting is a residual based AR bootstrap that ensures that bootstrap replicate time series are created under the null irrespective of whether the originally observed series obeys the null hypothesis or not. Simulation studies wherein we examine the performance of our proposed method are given; we evaluate our method’s performance on ARMA(1,1) models with varying configurations for size and power performance. We also propose a novel data dependent lag selection technique that uses bootstrap data under the null to select an optimal lag length; the performance of our method is compared to existing lag length selection criteria.
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- Award ID(s):
- 2413718
- PAR ID:
- 10597110
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Stats
- Volume:
- 7
- Issue:
- 4
- ISSN:
- 2571-905X
- Page Range / eLocation ID:
- 1226 to 1244
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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