Structural break analysis for spectrum and trace of covariance operators?

Aue, Alexander; Rice, Gregory E.; Sönmez, Ozan

doi:10.48550/arxiv.1804.03255

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where • now denotes the L 2 norm on L 2 ([0, 1] 2 ), see also the proof of Lemma A.3 in Aue et al (2018) for similar arguments. Now going through the proofs in Berkes et al (2013) we find that most of their results hold for spaces of square integrable functions on general subsets of R d and that there is no special structure of T = [0, 1] that they use.…”

Section: B4 Outline Of Proofs For Sectionmentioning

confidence: 99%

Testing relevant hypotheses in functional time series via self-normalization

Dette¹,

Kokot²,

Volgushev³

2018

Preprint

View full text Add to dashboard Cite

In this paper we develop methodology for testing relevant hypotheses about functional time series in a tuning-free way. Instead of testing for exact equality, for example for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two sample problem this means that an L 2 -distance between the two mean functions is smaller than a pre-specified threshold. For such hypotheses self-normalization, which was introduced by Shao (2010) and Shao and Zhang (2010) and is commonly used to avoid the estimation of nuisance parameters, is not directly applicable. We develop new self-normalized procedures for testing relevant hypotheses in the one sample, two sample and change point problem and investigate their asymptotic properties. Finite sample properties of the proposed tests are illustrated by means of a simulation study and data examples. Our main focus is on functional time series, but extensions to other settings are also briefly discussed.

show abstract

Section: B4 Outline Of Proofs For Sectionmentioning

confidence: 99%