Quantifying deviations from separability in space-time functional processes

Simple item page
dc.contributor.authorDette, Holger
dc.contributor.authorDierickx, Gauthier
dc.contributor.authorKutta, Tim
dc.date.accessioned2020-03-31T09:11:42Z
dc.date.available2020-03-31T09:11:42Z
dc.date.issued2020
dc.description.abstractThe estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors. Powerful tests for this assumption have been proposed in the literature. However, as real world systems, such as climate data are notoriously inseparable, validating this assumption by statistical tests, seems inherently questionable. In this paper we present an alternative approach: By virtue of separability measures, we quantify how strongly the data’s covariance operator diverges from a separable approximation. Confidence intervals localize these measures with statistical guarantees. This method provides users with a flexible tool, to weigh the computational gains of a separable model against the associated increase in bias. As separable approximations we consider the established methods of partial traces and partial products, and develop weak convergence principles for the corresponding estimators. Moreover, we also prove such results for estimators of optimal, separable approximations, which are arguably of most interest in applications. In particular we present for the first time statistical inference for this object, which has been confined to estimation previously. Besides confidence intervals, our results encompass tests for approximate separability. All methods proposed in this paper are free of nuisance parameters and do neither require computationally expensive resampling procedures nor the estimation of nuisance parameters. A simulation study underlines the advantages of our approach and its applicability is demonstrated by the investigation of German annual temperature data.en
dc.identifier.urihttp://hdl.handle.net/2003/39075
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-20994
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;9/2020en
dc.subjectspace-time processesen
dc.subjectself-normalizationen
dc.subjectoptimal approximationen
dc.subjectpartial tracesen
dc.subjectapproximate separabilityen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleQuantifying deviations from separability in space-time functional processesen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
DP_0920_SFB823_Dette_Dierickx_Kutta.pdf
Size:
1009.17 KB
Format:
Adobe Portable Document Format
Description:
DNB
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
4.85 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Sonderforschungsbereich (SFB) 823