Consistency of a hybrid block bootstrap for distribution and variance estimation for sample quantiles of weakly dependent sequences

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Title: Consistency of a hybrid block bootstrap for distribution and variance estimation for sample quantiles of weakly dependent sequences
Author(s): Young, GA
Lee, S
Kuffner, T
Item Type: Journal Article
Abstract: 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 (1995), among others. However, for nonsmooth functionals, such as quantiles, much less is known. Existing results, due to Sun & Lahiri (2006), regarding strong consistency for distribution and variance estimation via the moving block bootstrap (MBB) require that b→∞, where b=⌊n/ℓ⌋ is the number of resampled blocks to be pasted together to form the bootstrap data series, n is the available sample size, and ℓ is the block length. Here we show that, in fact, weak consistency holds for any b such that 1≤b=O(n/ℓ). In other words we show that a hybrid between the subsampling bootstrap (b=1) and MBB is consistent. Empirical results illustrate the performance of hybrid block bootstrap estimators for varying numbers of blocks.
Publication Date: 14-Mar-2018
Date of Acceptance: 18-Mar-2017
URI: http://hdl.handle.net/10044/1/50036
DOI: https://dx.doi.org/10.1111/anzs.12206
ISSN: 1369-1473
Publisher: Wiley
Start Page: 103
End Page: 114
Journal / Book Title: Australian and New Zealand Journal of Statistics
Volume: 60
Issue: 1
Copyright Statement: © 2018 Australian Statistical Publishing Association Inc. Published by John Wiley & Sons Australia Pty Ltd.
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
asymptotics
nonsmooth functional
resampling
strong mixing
subsampling
STATIONARY OBSERVATIONS
VALUES
0104 Statistics
1403 Econometrics
Statistics & Probability
Publication Status: Published
Embargo Date: 2019-03-14
Online Publication Date: 2018-03-14
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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