Data projections by skewness maximization under scale mixtures of skew-normal vectors

Multivariate scale mixtures of skew-normal distributions are flexible models that account for the non-normality of data by means of a tail weight parameter and a shape vector representing the asymmetry of the model in a directional fashion. Its stochastic representation involves a skew-normal vector...

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Bibliographic Details
Published in:Advances in data analysis and classification 2020-06, Vol.14 (2), p.435-461
Main Authors: Arevalillo, Jorge M., Navarro, Hilario
Format: Article
Language:English
Subjects:
Asymmetry
Chemistry and Earth Sciences
Computer Science
Computer simulation
Data Mining and Knowledge Discovery
Economics
Finance
Health Sciences
Humanities
Insurance
Law
Management
Mathematics and Statistics
Medicine
Normal distribution
Normality
Physics
Regular Article
Skewed distributions
Skewness
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
Weight
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Summary:Multivariate scale mixtures of skew-normal distributions are flexible models that account for the non-normality of data by means of a tail weight parameter and a shape vector representing the asymmetry of the model in a directional fashion. Its stochastic representation involves a skew-normal vector and a non negative mixing scalar variable, independent of the skew-normal vector, that injects tail weight behavior into the model. In this paper we look into the problem of finding the projection that maximizes skewness for vectors that follow a scale mixture of skew-normal distribution; when a simple condition on the moments of the mixing variable is fulfilled, it can be shown that the direction yielding the maximal skewness is proportional to the shape vector. This finding stresses the directional nature of the shape vector to regulate the asymmetry; it also provides the theoretical foundations motivating the skewness based projection pursuit problem in this class of distributions. Some examples that illustrate the application of our results are also given; they include a simulation experiment with artificial data, which sheds light on the usefulness and implications of our results, and the application to real data.
ISSN:1862-5347
1862-5355
DOI:10.1007/s11634-020-00388-6