Functional Sieve Bootstrap for the Partial Sum Process with Application to Change-Point Detection

Fuente: arXiv
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Autores principales: Paparoditis, Efstathios, Wegner, Lea, Wendler, Martin
Formato: Preprint
Publicado: 2024
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author Paparoditis, Efstathios
Wegner, Lea
Wendler, Martin
author_facet Paparoditis, Efstathios
Wegner, Lea
Wendler, Martin
contents This paper applies the functional sieve bootstrap (FSB) to estimate the distribution of the partial sum process for time series stemming from a weakly stationary functional process. Consistency of the FSB procedure under weak assumptions on the underlying functional process is established. This result allows for the application of the FSB procedure to testing for a change-point in the mean of a functional time series using the CUSUM-statistic. We show that the FSB asymptotically correctly estimates critical values of the CUSUM-based test under the null-hypothesis. Consistency of the FSB-based test under local alternatives also is proven. The finite sample performance of the procedure is studied via simulations.
format Preprint
id arxiv_https___arxiv_org_abs_2408_05071
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Functional Sieve Bootstrap for the Partial Sum Process with Application to Change-Point Detection
Paparoditis, Efstathios
Wegner, Lea
Wendler, Martin
Statistics Theory
This paper applies the functional sieve bootstrap (FSB) to estimate the distribution of the partial sum process for time series stemming from a weakly stationary functional process. Consistency of the FSB procedure under weak assumptions on the underlying functional process is established. This result allows for the application of the FSB procedure to testing for a change-point in the mean of a functional time series using the CUSUM-statistic. We show that the FSB asymptotically correctly estimates critical values of the CUSUM-based test under the null-hypothesis. Consistency of the FSB-based test under local alternatives also is proven. The finite sample performance of the procedure is studied via simulations.
title Functional Sieve Bootstrap for the Partial Sum Process with Application to Change-Point Detection
topic Statistics Theory
url https://arxiv.org/abs/2408.05071