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PRODID:https://murmitoyen.com/events/vanille/udem/
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UID:69dd14ce82d62
DTSTAMP:20260413T120742
DTSTART:20160211T153000
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URL:https://murmitoyen.com/events/vanille/udem/detail/675073-outlier-detect
 ion-for-functional-data-using-principal-components
LOCATION:Université de Montréal - Pavillon André-Aisenstadt\, 2920\, che
 min de la Tour\, Montréal\, QC\, Canada\, H3T 1N8
SUMMARY:Outlier Detection for Functional Data Using Principal Components
DESCRIPTION:Conférence de Matìas Salibián-Barrera\, University of Britis
 h Columbia
\nRésuméPrincipal components analysis is a widely used techni
 que that provides an optimal lower-dimensional approximation to multivaria
 te observations. In the functional case\, a new characterization of ellipt
 ical distributions on separable Hilbert spaces allows us to obtain an equi
 valent stochastic optimality property for the principal component subspace
 s of random elements on separable Hilbert spaces. This property holds even
  when second moments do not exist.
\nThese lower-dimensional approximation
 s can be very useful in identifying potential outliers among high-dimensio
 nal or functional observations. In this talk we propose a new class of rob
 ust estimators for principal components\, which is consistent for elliptic
 al random vectors\, and Fisher-consistent for elliptically distributed ran
 dom elements on arbitrary Hilbert spaces. We illustrate our method on two 
 real functional data sets\, where the robust estimator is able to discover
  atypical observations in the data that would have been missed otherwise.

 \nThis talk is the result of recent collaborations with Graciela Boente (B
 uenos Aires\, Argentina) and David Tyler (Rutgers\, USA).
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