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Local statistical modeling via a cluster-weighted approach with elliptical distributions. (English) Zbl 1360.62335

Summary: Cluster-weighted modeling (CWM) is a mixture approach to modeling the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both theoretical and numerical point of view; in particular, we show that Gaussian CWM includes mixtures of distributions and mixtures of regressions as special cases. Further, we introduce CWM based on Student-\(t\) distributions, which provides a more robust fit for groups of observations with longer than normal tails or noise data. Theoretical results are illustrated using some empirical studies, considering both simulated and real data. Some generalizations of such models are also outlined.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62F10 Point estimation
62J05 Linear regression; mixed models

Software:

CapeML; flexmix
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References:

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