Change-point detection and bootstrap for Hilbert space valued random fields

Béatrice Bucchia and Martin Wendler

Journal of Multivariate Analysis, 2017, vol. 155, issue C, 344-368

Abstract: The problem of testing for the presence of epidemic changes in random fields is investigated. In order to be able to deal with general changes in the marginal distribution, a Cramér–von Mises type test is introduced which is based on Hilbert space theory. A functional central limit theorem for ρ-mixing Hilbert space valued random fields is proven. In order to avoid the estimation of the long-run variance and obtain critical values, Shao’s dependent wild bootstrap method is adapted to this context. For this, a joint functional central limit theorem for the original and the bootstrap sample is shown. Finally, the theoretic results are supplemented by a short simulation study.

Keywords: Change-point detection; Dependent wild bootstrap; FCLT for Hilbert space valued r.v.; Random fields (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.jmva.2017.01.007

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