A Distribution-Free Method of Interval Estimation for Unsigned Directional Data
针对大样本无符号方向数据，提出一种矩估计方法，其点估计与Bingham分布下的极大似然估计一致，但区间估计计算更简单，并通过数值例子验证了区域估计的相似性。
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).