Independence tests for circular data

Abstract

In many diverse scientific fields, the measurements are directions. In the two-dimensional case, directions can be represented as points on the circumference of a unit circle centered at the origin or as unit vectors connecting the origin to these points, named circular data. The numerical representation of circular data as an angle or a unit vector is not necessarily unique, because of that many of the usual linear techniques and measures are often misleading. In this regard, we propose a new class of tests whose test statistic is the distance correlation coefficient based on energy distance. Also, we propose two generalizations based on kernel functions. For all test statistics, asymptotic properties are obtained and an empirical study is conducted.