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SUMMARY:Tests for separability in nonparametric covariance operators of ra
 ndom surfaces - Shahin Tavakoli (University of Warwick)
DTSTART:20180612T100000Z
DTEND:20180612T110000Z
UID:TALK107266@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The assumption of separability of the covariance operator for 
 a random image or hypersurface can be of substantial use in applications\,
  especially in situations where the accurate estimation of the full covari
 ance structure is unfeasible\, either for computational reasons or due to 
 a small sample size. However\, inferential tools to verify this assumption
  are somewhat lacking in high-dimensional or functional settings where thi
 s assumption is most relevant. We propose here to test separability by foc
 using on K-dimensional projections of the difference between the covarianc
 e operator and its nonparametric separable approximation. The subspace we 
 project onto is one generated by the eigenfunctions estimated under the se
 parability hypothesis\, negating the need to ever estimate the full non-se
 parable covariance. We show that the rescaled difference of the sample cov
 ariance operator with its separable approximation is asymptotically Gaussi
 an. As a by-product of this result\, we derive asymptotically pivotal test
 s under Gaussian assumptions\, and propose bootstrap methods for approxima
 ting the distribution of the test statistics when multiple eigendirections
  are taken into account. We probe the finite sample performance through si
 mulations studies\, and present an application to log-spectrogram images f
 rom a phonetic linguistics dataset.  This is joint work with Davide Pigoli
  (KCL) and John Aston (Cambridge)
LOCATION:Seminar Room 2\, Newton Institute
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