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Biometrika 1997 84(3):717-726; doi:10.1093/biomet/84.3.717
© 1997 by Biometrika Trust
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A decentred predictor for circular-circular regression

LOUIS-PAUL RIVEST

Département de mathématiques et de statistique, Université Laval Ste-Foy, Québec G1K 7P4, Canada e-mail: lpr{at}mat.ulaval.ca

This paper considers the prediction of a y-angle, given an x-angle in a circular-circular regression. The predictor under study is a rotation of the decentred x-angle, denned as the direction of the sum of the unit vector corresponding to angle x plus a decentring vector. The parameters are defined as those which maximise the average residual cosine. This predictor is shown to perform well when the data come from a bivariate von Mises distribution or from a wrapped bivariate normal model. The large sample distributions of maximum cosine estimators are derived. Tests of fit for the rotational model, which predicts y by a rotation of x, and for the independence model where y is not related to x are presented. The proposed methods are illustrated by the analysis of an earthquake dataset where the direction of ground movement is regressed on the direction of steepest descent.

Key Words: Angular regression • Directional data • Earthquake ground movement • Test of independence • Von Mises distribution • Wrapped normal distribution


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