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 |
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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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