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CATEGORIES:Statistics
SUMMARY:Dynamic functional principal components - Siegfrie
d Hörmann\, Université libre de Bruxelles
DTSTART;TZID=Europe/London:20141128T160000
DTEND;TZID=Europe/London:20141128T170000
UID:TALK54676AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/54676
DESCRIPTION:Data in many fields of science are sampled from pr
ocesses that can most naturally be described as fu
nctional. Examples include growth curves\, tempera
ture curves\, curves of financial transaction data
and patterns of pollution data. Functional data a
nalysis (FDA) is concerned with the statistical an
alysis of such data.\n\nAn important tool in many
empirical and theoretical problems related to FDA
is the functional principal analysis (FPCA) which
allows to represent or approximate curves in low d
imension. It is certainly the most common approach
to obtain dimension reduction for functional data
. In fact\, it achieves in some sense optimal dime
nsion reduction if data are independent. However\,
it is all but uncommon that functional data are s
erially correlated.\n\nA typical example is if the
observations are segments from a continuous time
process (e.g. days). Then\, although cross-section
ally uncorrelated for a fixed observation\, the cl
assical FPC-score vectors have non-diagonal cross-
correlations. This means that we cannot analyze th
em componentwise (like in the i.i.d. case)\, but w
e need to consider them as vector time series whic
h are less easy to handle and to interpret. In par
ticular\, a functional principal component with sm
all eigenvalue\, hence negligible instantaneous im
pact on some observation\, may have a major impact
on the lagged values. Regular FPCs\, thus\, in a
time series context\, will not lead to an adequate
dimension reduction technique\, as they do in the
i.i.d. case. This motivates the development of a
time series version of functional PCA. The idea is
to transform the (possibly infinite dimensional)
functional time series\, into a vector time series
(of low dimension 3 or 4\, say)\, where the indiv
idual component processes are mutually uncorrelate
d\, and explain a bigger part of the dynamics and
variability of the original process.\n\nIn this ta
lk we will propose such a dynamic version of FPCA
for general data structures (Hilbertian data) and
study its properties. An empirical analysis and a
real data example will be given.\n\nThe talk is ba
sed on joint work with Lukasz Kidziński (EPFL) and
Marc Hallin (ULB).
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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