BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Assessing the finite-dimensionality of functional data - Celine Vi
 al (Rennes)
DTSTART:20071130T140000Z
DTEND:20071130T150000Z
UID:TALK8685@talks.cam.ac.uk
CONTACT:6845
DESCRIPTION:If a problem in functional data analysis is low-dimensional th
 en the methodology for its solution can often be reduced to relatively con
 ventional techniques in multivariate analysis. Hence\, there is intrinsic 
 interest in assessing the finite-dimensionality of functional data. We sho
 w that this problem has several unique features. From some viewpoints the 
 problem is trivial\, in the sense that continuously-distributed functional
  data which are exactly finite-dimensional are immediately recognisable as
  such\, if the sample size is sufficiently large. However\, in practice\, 
 functional data are almost always observed with noise\, for example result
 ing from rounding or experimental error. Then the problem is almost insolu
 bly difficult. In such cases a part of the average noise variance is confo
 unded with the true signal\, and is not identifiable. However\, it is poss
 ible to define the unconfounded part of the noise variance. This represent
 s the best possible lower bound to all potential values of average noise v
 ariance\, and is estimable in low-noise settings. Moreover\, bootstrap met
 hods can be used to describe the reliability of estimates of unconfounded 
 noise variance\, under the assumption that the signal is finite-dimensiona
 l. Motivated by these ideas\, we suggest techniques for assessing the fini
 teness of dimensionality. In particular\, we show how to construct a criti
 cal point $\\hat{v}_q$ such that\, if the distribution of our functional d
 ata has fewer than q - 1 degrees of freedom\, then we should be prepared t
 o assume that the average variance of the added noise is at least $\\hat{v
 }_q$ If this level seems too high then we must conclude that the dimension
  is at least q - 1. We show that simpler\, more conventional techniques\, 
 based on hypothesis testing\, are generally not effective. \n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
END:VEVENT
END:VCALENDAR