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CATEGORIES:Statistics
SUMMARY:High-Dimensional Covariance Structure Estimation -
Zhao Ren\, Yale University
DTSTART;TZID=Europe/London:20140228T140000
DTEND;TZID=Europe/London:20140228T150000
UID:TALK51223AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51223
DESCRIPTION:Covariance matrices play a central role in multiva
riate statistical analysis. A wide range of statis
tical methodologies\, including clustering analysi
s\, principal component analysis\, linear and quad
ratic discriminant analysis\, Gaussian graphical m
odels require the knowledge of the covariance or p
recision structure.\n\nThe first half of the talk
is presented in a chalk talk style. We talk about
some motivations and challenges of estimating cova
riance matrices in the high-dimensional setting. T
hen we briefly review some of the developments in
estimation of covariance and precision matrices in
the past decade. Several classes of covariance an
d precision matrices are discussed. We pay special
attention to optimality theory.\n\nThe second hal
f of the talk focuses on one specific class: Toepl
itz covariance structure\, which is used in the an
alysis of stationary time series and a wide range
of applications including radar imaging\, target d
etection and speech recognition. We consider optim
al estimation of large Toeplitz covariance matrice
s under the spectral norm. Minimax rate of converg
ence is established for two commonly used paramete
r spaces. The minimax upper bound is obtained by s
tudying the properties of tapering and banding est
imators. The minimax lower bound is obtained by fi
rst constructing a more informative model for whic
h independent random variables are observed\, and
then deriving a lower bound for the more informati
ve model by carefully constructing a collection of
least favorable spectral densities and applying F
ano's Lemma.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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