On optimal block resampling for Gaussian-subordinated long-range dependent processes

dc.contributor.author Miller-Chang, Yeng
dc.contributor.author Nordman, Daniel
dc.contributor.department Statistics
dc.contributor.majorProfessor Daniel J. Nordman
dc.date 2020-06-15T19:59:59.000
dc.date.accessioned 2020-06-30T01:35:47Z
dc.date.available 2020-06-30T01:35:47Z
dc.date.copyright Wed Jan 01 00:00:00 UTC 2020
dc.date.issued 2020-01-01
dc.description.abstract <p>Block resampling methods are useful for nonparametrically approximating the sampling distributions of statistics from dependent data. Much research has focused on weakly dependent time processes and understanding the large-sample properties of block subsampling (and bootstrap) methods, which has helped to inform implementation through the choice of the best block sizes, particularly for inference about sample means (as a prototypical statistic). However, relatively little is known about resampling performance and best block sizes under strong- or long-range time dependence. We consider a broad class of strongly dependent and possibly non-linear time series, which are formed by a transformation of a stationary long-memory Gaussian series. We determine the estimation error and best block sizes for subsampling (or block bootstrap) variance estimation of the sample mean from such processes. Explicit expressions are given for the bias and variance of block subsampling/bootstrap estimators with overlapping or non-overlapping blocks, which depend intricately amount of non-linearity in the time series as well as a strong dependence coefficient. In contrast, for weakly dependent time series, bias/variance properties of subsampling/bootstrap estimators are completely invariant to the degree of non-linearity in the time series (i.e., a non-issue), and overlapping blocks always induce better performance than non-overlapping blocks regardless of the exact block length choice. However, neither of these aspects remains true for transformation-based long memory time series and, perhaps surprisingly, <em>any</em> amount of non-linearity in the time series destroys advantages of overlapping blocks.</p>
dc.format.mimetype PDF
dc.identifier archive/lib.dr.iastate.edu/creativecomponents/534/
dc.identifier.articleid 1543
dc.identifier.contextkey 17386384
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath creativecomponents/534
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/17105
dc.source.bitstream archive/lib.dr.iastate.edu/creativecomponents/534/Creative_Component.pdf|||Sat Jan 15 00:51:32 UTC 2022
dc.subject.disciplines Longitudinal Data Analysis and Time Series
dc.subject.keywords Block size
dc.subject.keywords FARIMA
dc.subject.keywords Fractional Gaussian
dc.subject.keywords moving block bootstrap
dc.subject.keywords variance estimation
dc.title On optimal block resampling for Gaussian-subordinated long-range dependent processes
dc.type article
dc.type.genre creativecomponent
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca
thesis.degree.discipline Statistics
thesis.degree.level creativecomponent
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