Constrained monotone EM algorithms for mixtures of multivariate t distributions

F. Greselin; S. Ingrassia

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Constrained monotone EM algorithms for mixtures of multivariate t distributions

机译：多元t分布混合的约束单调EM算法

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摘要

Mixtures of multivariate t distributions provide a robust parametric extension to the fitting of data with respect to normal mixtures. In presence of some noise component, potential outliers or data with longer-than-normal tails, one way to broaden the model can be provided by considering t distributions. In this framework, the degrees of freedom can act as a robustness parameter, tuning the heaviness of the tails, and downweighting the effect of the outliers on the parameters estimation. The aim of this paper is to extend to mixtures of multivariate elliptical distributions some theoretical results about the likelihood maximization on constrained parameter spaces. Further, a constrained monotone algorithm implementing maximum likelihood mixture decomposition of multivariate t distributions is proposed, to achieve improved convergence capabilities and robustness. Monte Carlo numerical simulations and a real data study illustrate the better performance of the algorithm, comparing it to earlier proposals.

机译：多元t分布的混合为相对于正常混合的数据拟合提供了鲁棒的参数扩展。在存在某些噪声成分，潜在异常值或尾部比正常长的数据时，可以通过考虑t分布来提供一种扩展模型的方法。在此框架中，自由度可以用作鲁棒性参数，调整尾部的沉重程度以及降低异常值对参数估计的影响。本文的目的是将有关参数空间上似然最大化的一些理论结果扩展到多元椭圆分布的混合。此外，提出了一种约束单调算法，该算法实现了多元t分布的最大似然混合分解，以提高收敛能力和鲁棒性。蒙特卡洛数值模拟和实际数据研究证明了该算法的更好性能，并将其与早期建议进行了比较。

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来源
《Statistics and computing》 |2010年第1期|9-22|共14页
作者
F. Greselin; S. Ingrassia;
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作者单位

Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali, Universita di Milano Bicocca, Piazza dell'Ateneo Nuovo, 1, 20126 Milano, Italy;

Dipartimento di Economia e Metodi Quantitativi, Universita di Catania, Corso Italia, 55, 95129 Catania, Italy;

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原文格式 PDF
正文语种 eng
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关键词
finite mixture models; EM algorithm; t distribution; clustering;

机译：有限混合模型;EM算法;t分布聚类;

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1. Constrained monotone EM algorithms for finite mixture of multivariate Gaussians [J] . Salvatore Ingrassia, Roberto Rocci Computational statistics & data analysis . 2007,第11期

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2. Constrained monotone EM algorithms for finite mixture of multivariate Gaussians [J] . Salvatore Ingrassia, Roberto Rocci Computational statistics & data analysis . 2007,第11期

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4. A minimax approach to development of robust discrimination algorithms for multivariate mixture distributions [C] . Flick, T.E., Jones, . 1988

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7. Constrained monotone em algorithms for finite mixture of multivariate gaussians [O] . Salvatore Ingrassiaa, Roberto Roccib 2016

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8. Monotone Hazard and Failure Rates for Multivariate Distributions. [R] . block,henry w. 1975

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Constrained monotone EM algorithms for mixtures of multivariate t distributions

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