BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Statistics
SUMMARY:What is the dimension of a stochastic process? - V
ictor Panaretos (EPFL)
DTSTART;TZID=Europe/London:20180607T160000
DTEND;TZID=Europe/London:20180607T170000
UID:TALK101968AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/101968
DESCRIPTION:How can we determine whether a mean-square continu
ous stochastic process is\, in fact\, finite-dimen
sional\, and if so\, what its actual dimension is?
And how can we do so at a given level of confiden
ce? This question is central to a great deal of me
thods for functional data analysis\, which require
low-dimensional representations whether by functi
onal PCA or other methods. The difficulty is that
the determination is to be made on the basis of ii
d replications of the process observed discretely
and with measurement error contamination. This add
s a ridge to the empirical covariance\, obfuscatin
g the underlying dimension. We build a matrix-comp
letion-inspired test procedure that circumvents th
is issue by measuring the best possible least squa
re fit of the empirical covariance's off-diagonal
elements\, optimised over covariances of given fin
ite rank. For a fixed grid of sufficient size\, we
determine the statistic's asymptotic null distrib
ution as the number of replications grows. We then
use it to construct a bootstrap implementation of
a stepwise testing procedure for the collection o
f hypotheses formalising the question at hand. The
procedure involves no tuning parameters or pre-sm
oothing\, is indifferent to the homoskedasticity o
r lack of it in the measurement errors\, and does
not assume a low-noise regime. Based on joint work
with Anirvan Chakraborty (EPFL).
LOCATION:MR11
CONTACT:Quentin Berthet
END:VEVENT
END:VCALENDAR