A distribution-free method of interval estimation for unsigned directional data

A method of moments is suggested for large samples of unsigned directional data. The point estimators obtained coincide with the natural estimates obtained from maximum likelihood estimation if the data have a Bingham distribution. However, the calculations necessary for interval and regional estimation are considerably simpler. The statistical analysis is based upon the asymptotic sampling properties of principal components in nonnormal populations (Davis, 1977; Tyler, 1981). A numerical example first treated by Bingham (1974) is examined and found to yield very similar regional estimates. The hypothesis of rotational symmetry is discounted by using a test statistic suggested by Watson (1965).