On the number of modes of finite mixtures of elliptical distributions

Alexandrovich, G., Holzmann, H. and Ray, S. (2013) On the number of modes of finite mixtures of elliptical distributions. In: Lausen, B., Van den Poel, D. and Ultsch, A. (eds.) Algorithms from and for Nature and Life: Classification and Data Analysis. Series: Studies in Classification, Data Analysis, and Knowledge Organization, 2. Springer International Publishing, pp. 49-57. ISBN 9783319000350 (doi:10.1007/978-3-319-00035-0_4)

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Abstract

We extend the concept of the ridgeline from Ray and Lindsay (Ann Stat 33:2042–2065, 2005) to finite mixtures of general elliptical densities with possibly distinct density generators in each component. This can be used to obtain bounds for the number of modes of two-component mixtures of t distributions in any dimension. In case of proportional dispersion matrices, these have at most three modes, while for equal degrees of freedom and equal dispersion matrices, the number of modes is at most two. We also give numerical illustrations and indicate applications to clustering and hypothesis testing.

Item Type:Book Sections
Additional Information:The final publication is available at link.springer.com.
Keywords:inite mixtures, number of modes, elliptical distributions, t distribution
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ray, Professor Surajit
Authors: Alexandrovich, G., Holzmann, H., and Ray, S.
Subjects:H Social Sciences > HA Statistics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Publisher:Springer International Publishing
ISBN:9783319000350
Copyright Holders:Copyright © 2013 Springer International Publishing Switzerland
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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