Double block bootstrap confidence intervals for dependent data

The block bootstrap confidence interval for dependent data can outperform the conventional normal approximation only with nontrivial studentization which, in the case of complicated statistics, calls for specialist treatment and often results in unstable endpoints. We propose two double block bootst...

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Bibliographic Details
Published in:Biometrika 2009-06, Vol.96 (2), p.427-443
Main Authors: Lee, Stephen M. S., Lai, P. Y.
Format: Article
Language:English
Subjects:
Accuracy
Analytical estimating
Applications
Approximation
Autocorrelation
Biology, psychology, social sciences
Bootstrap method
Calibration
Confidence interval
Coverage calibration
Double block bootstrap
Estimates
Estimators
Exact sciences and technology
General topics
Mathematics
Modeling
Musical intervals
Nonparametric inference
p-value
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistical variance
Statistics
Studentization
Studies
Theorems
Time series
Weakly dependent
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Summary:The block bootstrap confidence interval for dependent data can outperform the conventional normal approximation only with nontrivial studentization which, in the case of complicated statistics, calls for specialist treatment and often results in unstable endpoints. We propose two double block bootstrap approaches for improving the accuracy of the block bootstrap confidence interval under very general conditions. The first approach calibrates the nominal coverage level and the second calculates studentizing factors directly from a block bootstrap series without the need for nontrivial analytical treatment. We prove that the two approaches reduce the coverage error of the block bootstrap interval by an order of magnitude with simple tuning of block lengths at the two block bootstrapping levels. Empirical properties of the procedures are investigated by simulations and application to an econometric time series.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asp018