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SUMMARY:Estimating a directional trend from noisy directional data - Rudy 
 Beran\, University of California Davis
DTSTART:20140625T144500Z
DTEND:20140625T151500Z
UID:TALK53119@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:Consider measured positions of the paleomagnetic north pole ov
 er time. Each\nmeasured position may be viewed as a direction\, expressed 
 as a unit vector in three\ndimensions. The abstract problem is to estimate
  an underlying trend from an\nobserved sequence of unit vectors in q-dimen
 sions\, each indexed by an ordinal\ncovariate and measured with random err
 or. In this sequence\, mean directions are\nexpected to be close to one an
 other at nearby covariate values. A simple trend\nestimator that respects 
 the geometry of the sphere is to compute a running average\nover the covar
 iate-ordered observed direction vectors\, then normalize these average\nve
 ctors to unit length. This talk treats a considerably richer class of comp
 eting\ndirectional trend estimators that respect spherical geometry. The a
 nalysis relies on a\nnonparametric error model for directional data that m
 akes no symmetry or other\nshape assumptions. Good trend estimators are se
 lected through calculations of\nestimated risk under the error model. Empi
 rical process theory underlies claims that\nthe estimated risks are trustw
 orthy surrogates for the unknown risks of competing\ndirectional trend est
 imators.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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