Abstract
This article suggests a linear functional relationship model for comparing two sets of circular data subject to unobservable errors. Unlike the corresponding and relatively well-studied model for linear data, maximum likelihood estimation for this model is very complicated and no explicit solutions are possible. Using a numerical approximation, we are able to solve the likelihood equations approximately, and to obtain good approximations to the likelihood estimates of the parameters. The quality of our estimates and the feasibility of the estimation method are illustrated via simulation. By establishing a parallel with the model for linear data, we are able to explain the various problems occurring in the process of estimation and to substantiate our numerical results. The interest in the model arose in connection with the study of ocean wave data; an application to such data is also given.
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