Some Linear Model Techniques for Analyzing Small Circle Spherical Data

• Main Author: Louis-Paul Rivest
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Key words and phrases; Conical folds; Directional data; Fisher distribution; Girdle distribution; Rotationally symmetric distribution; Spherical ellipse; Watson distribution; Elephant Seals
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.6286; http://www.mat.ulaval.ca/cjs/pub/rivest/rivest.pdf

The author investigates least squares as a method for fitting small circle models to a sample of unit vectors in R³. He highlights a local linear model underlying the estimation of the circle's parameters. This model is used to construct an estimation algorithm and regression type inference procedures for the circle's parameters. It makes it possible to compare the fit of a small circle with that of a spherical ellipse. The limitations of the least squares approach are emphasized: when the errors are bounded away from 0, the least squares estimators are not consistent as the sample size goes to infinity. Two examples, concerned with the migration of elephant seals and with the classification of geological folds, are analyzed using the linear model techniques proposed in this work.