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- Title
Consistency of a hybrid block bootstrap for distribution and variance estimation for sample quantiles of weakly dependent sequences.
- Authors
Kuffner, Todd A.; Lee, Stephen M. S.; Young, G. A.
- Abstract
Summary: Consistency and optimality of block bootstrap schemes for distribution and variance estimation of smooth functionals of dependent data have been thoroughly investigated by Hall, Horowitz & Jing ( ), among others. However, for nonsmooth functionals, such as quantiles, much less is known. Existing results, due to Sun & Lahiri ( ), regarding strong consistency for distribution and variance estimation via the moving block bootstrap (MBB) require that <italic>b</italic>→∞, where <italic>b</italic>=⌊<italic>n</italic>/ℓ⌋ is the number of resampled blocks to be pasted together to form the bootstrap data series, <italic>n</italic> is the available sample size, and ℓ is the block length. Here we show that, in fact, weak consistency holds for any <italic>b</italic> such that 1≤<italic>b</italic>=<italic>O</italic>(<italic>n</italic>/ℓ). In other words we show that a hybrid between the subsampling bootstrap (<italic>b</italic>=1) and MBB is consistent. Empirical results illustrate the performance of hybrid block bootstrap estimators for varying numbers of blocks.
- Subjects
CLASSICAL statistics; QUANTILES; NONSMOOTH optimization; RESAMPLING (Statistics); STATISTICAL bootstrapping
- Publication
Australian & New Zealand Journal of Statistics, 2018, Vol 60, Issue 1, p103
- ISSN
1369-1473
- Publication type
Article
- DOI
10.1111/anzs.12206