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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:TALK106792AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/106792
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:INI IT
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