Rumcheva Pavlina, Presnell Brett
U.S. Centers for Disease Control and Prevention and University of Florida.
Aust N Z J Stat. 2017 Mar 1;59(1):119-135. doi: 10.1111/anzs.12183.
A multi-sample test for equality of mean directions is developed for populations having Langevin-von Mises-Fisher distributions with a common unknown concentration. The proposed test statistic is a monotone transformation of the likelihood ratio. The high-concentration asymptotic null distribution of the test statistic is derived. In contrast to previously suggested high-concentration tests, the high-concentration asymptotic approximation to the null distribution of the proposed test statistic is also valid for large sample sizes with any fixed nonzero concentration parameter. Simulations of size and power show that the proposed test outperforms competing tests. An example with three-dimensional data from an anthropological study illustrates the practical application of the testing procedure.
针对具有共同未知浓度的Langevin-von Mises-Fisher分布的总体，开发了一种用于均值方向相等性的多样本检验。所提出的检验统计量是似然比的单调变换。推导了检验统计量的高浓度渐近零分布。与先前提出的高浓度检验不同，所提出的检验统计量的零分布的高浓度渐近近似对于具有任何固定非零浓度参数的大样本量也有效。大小和功效的模拟表明，所提出的检验优于其他竞争检验。一个来自人类学研究的三维数据示例说明了检验程序的实际应用。
