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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Tests for separability in nonparametric covariance
operators of random surfaces - Shahin Tavakoli (U
niversity of Warwick)
DTSTART;TZID=Europe/London:20180612T110000
DTEND;TZID=Europe/London:20180612T120000
UID:TALK107098AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/107098
DESCRIPTION:The assumption of separability of the covariance o
perator for a random image or hypersurface can be
of substantial use in applications\, especially in
situations where the accurate estimation of the f
ull covariance structure is unfeasible\, either fo
r computational reasons or due to a small sample s
ize. However\, inferential tools to verify this as
sumption are somewhat lacking in high-dimensional
or functional settings where this assumption is mo
st relevant. We propose here to test separability
by focusing on K-dimensional projections of the di
fference between the covariance operator and its n
onparametric separable approximation. The subspace
we project onto is one generated by the eigenfunc
tions estimated under the separability hypothesis\
, negating the need to ever estimate the full non-
separable covariance. We show that the rescaled di
fference of the sample covariance operator with it
s separable approximation is asymptotically Gaussi
an. As a by-product of this result\, we derive asy
mptotically pivotal tests under Gaussian assumptio
ns\, and propose bootstrap methods for approximati
ng the distribution of the test statistics when mu
ltiple eigendirections are taken into account. We
probe the finite sample performance through simula
tions studies\, and present an application to log-
spectrogram images from a phonetic linguistics dat
aset. This is joint work with Davide Pigoli (KCL)
and John Aston (Cambridge)
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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