An Efficient Test for Homogeneity of Mean Directions on the Hyper‐sphere
针对超球面方向数据的均值齐性检验，提出一种基于集成似然比检验（ILRT）的通用高效方法，在分散组群中表现优于传统检验，并通过向量心电图和药物开发中的成分数据分析等实例验证其应用。
Summary The paper aims to develop a universally implementable efficient test for testing homogeneity of mean directions of several independent hyper‐spherical populations. Conventional tests are valid only under highly concentrated and/or large‐size groups. Focusing on the popular Langevin distribution on a d ‐hyper‐sphere, the present work extends the very recent results for the circular case. The hurdle of the nuisance non‐location‐scale concentration parameter κ is overcome through a variant of the integrated likelihood ratio test (ILRT), yielding a simple and elegant test statistic. Analytically, second‐order accurate asymptotic chi‐squared distribution of ILRT is established. Extensive simulation study demonstrates that ILRT uniformly outperforms its peers, notably under highly dispersed groups, which is precisely the target parametric region, and is robust under a large class of alternate distributions. Five real‐life data analyses from diverse disciplines, including the emerging field of vectorcardiography and a novel application to compositional data analysis in the context of drug development, illustrate applications of the findings.