Estimating a directional trend from noisy directional data

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• Rudy Beran, University of California Davis
• Wednesday 25 June 2014, 15:45-16:15
• Centre for Mathematical Sciences, Meeting Room 2.

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Consider measured positions of the paleomagnetic north pole over time. Each measured position may be viewed as a direction, expressed as a unit vector in three dimensions. The abstract problem is to estimate an underlying trend from an observed sequence of unit vectors in q-dimensions, each indexed by an ordinal covariate and measured with random error. In this sequence, mean directions are expected to be close to one another at nearby covariate values. A simple trend estimator that respects the geometry of the sphere is to compute a running average over the covariate-ordered observed direction vectors, then normalize these average vectors to unit length. This talk treats a considerably richer class of competing directional trend estimators that respect spherical geometry. The analysis relies on a nonparametric error model for directional data that makes no symmetry or other shape assumptions. Good trend estimators are selected through calculations of estimated risk under the error model. Empirical process theory underlies claims that the estimated risks are trustworthy surrogates for the unknown risks of competing directional trend estimators.

This talk is part of the Probability Theory and Statistics in High and Infinite Dimensions series.

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