The skewness of mean-variance normal mixtures

被引:3
|
作者
Loperfido, Nicola [1 ]
机构
[1] Univ Urbino Carlo Bo, Dipartimento Econ Soc & Polit DESP, Via Saffi 42, I-61029 Urbino, PU, Italy
关键词
Mixture model; Projection pursuit; Skewness; Symmetrization; Tensor eigenvector; INDEPENDENT COMPONENT ANALYSIS; MULTIVARIATE SKEWNESS; PROJECTION PURSUIT; KURTOSIS; APPROXIMATION; DISTRIBUTIONS;
D O I
10.1016/j.jmva.2023.105242
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Mean-variance mixtures of normal distributions are very flexible: they model many nonnormal features, such as skewness, kurtosis and multimodality. Special cases include generalized asymmetric Laplace distributions, mixtures of two normal distributions with proportional covariance matrices, scale mixtures of normal distributions and normal distributions. This paper investigates the skewness of multivariate mean-variance normal mixtures. The special case of mixtures of two normal distributions with proportional covariance matrices is treated in greater detail. The paper derives the analytical forms of prominent measures of multivariate skewness and applies them to model-based clustering, normalizing linear transformations, projection pursuit and normality testing. The practical relevance of the theoretical results is assessed with both real and simulated data.(c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页数:18
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