Kurtosis test of modality for rotationally symmetric distributions on hyperspheres

JOURNAL OF MULTIVARIATE ANALYSIS

卷:178

Article

Kim, Byungwon¹  Schulz, Jorn^2,3  Jung, Sungkyu¹ 

[1] Seoul Natl Univ, Dept Stat, Seoul 08826, South Korea

[2] Univ Stavanger, Dept Math & Phys, N-4036 Stavanger, Norway

[3] Stavanger Univ Hosp, Dept Res, N-4068 Stavanger, Norway

关键词: Ball uniform distribution;    Directional data;    Exponential map;    Frechet mean;    Hausdorff moment;    Stieltjes moment;   

DOI  :  10.1016/j.jmva.2020.104603

来源: Elsevier

【 摘 要 】

A test of modality of rotationally symmetric distributions on hyperspheres is proposed. The test is based on a modified multivariate kurtosis defined for directional data on S-d. We first reveal a relationship between the multivariate kurtosis and the types of modality for Euclidean data. In particular, the kurtosis of a rotationally symmetric distribution with decreasing sectional density is greater than the kurtosis of the uniform distribution, while the kurtosis of that with increasing sectional density is less. For directional data, we show an asymptotic normality of the modified spherical kurtosis, based on which a large-sample test is proposed. The proposed test of modality is applied to the problem of preventing overfitting in non-geodesic dimension reduction of directional data. The proposed test is superior than existing options in terms of computation times, accuracy and preventing overfitting. This is highlighted by a simulation study and two real data examples. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free