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CATEGORIES:Probability Theory and Statistics in High and Infi
nite Dimensions
SUMMARY:Estimating a directional trend from noisy directio
nal data - Rudy Beran\, University of California D
avis
DTSTART;TZID=Europe/London:20140625T154500
DTEND;TZID=Europe/London:20140625T161500
UID:TALK53119AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53119
DESCRIPTION:Consider measured positions of the paleomagnetic n
orth pole over time. Each\nmeasured position may b
e viewed as a direction\, expressed as a unit vect
or in three\ndimensions. The abstract problem is t
o estimate an underlying trend from an\nobserved s
equence of unit vectors in q-dimensions\, each ind
exed by an ordinal\ncovariate and measured with ra
ndom error. In this sequence\, mean directions are
\nexpected to be close to one another at nearby co
variate values. A simple trend\nestimator that res
pects the geometry of the sphere is to compute a r
unning average\nover the covariate-ordered observe
d direction vectors\, then normalize these average
\nvectors to unit length. This talk treats a consi
derably richer class of competing\ndirectional tre
nd estimators that respect spherical geometry. The
analysis relies on a\nnonparametric error model f
or directional data that makes no symmetry or othe
r\nshape assumptions. Good trend estimators are se
lected through calculations of\nestimated risk und
er the error model. Empirical process theory under
lies claims that\nthe estimated risks are trustwor
thy surrogates for the unknown risks of competing\
ndirectional trend estimators.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
CONTACT:
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