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Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions

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Author Info

  • Salvatore Ingrassia

    ()

  • Simona Minotti

    ()

  • Giorgio Vittadini

    ()

Abstract

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. Copyright Springer Science+Business Media, LLC 2012

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File URL: http://hdl.handle.net/10.1007/s00357-012-9114-3
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Bibliographic Info

Article provided by Springer in its journal Journal of Classification.

Volume (Year): 29 (2012)
Issue (Month): 3 (October)
Pages: 363-401

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Handle: RePEc:spr:jclass:v:29:y:2012:i:3:p:363-401

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Web page: http://www.springerlink.com/link.asp?id=101794

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Related research

Keywords: Cluster-weighted modeling; Mixture models; Model-based clustering;

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References

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  1. Friedrich Leisch, . "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, American Statistical Association, vol. 11(i08).
  2. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods and Applications, Springer, vol. 20(2), pages 141-170, June.
  3. Ingrassia, Salvatore & Rocci, Roberto, 2007. "Constrained monotone EM algorithms for finite mixture of multivariate Gaussians," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5339-5351, July.
  4. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer, vol. 12(1), pages 21-55, March.
  5. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466.
  6. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
  7. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer, vol. 5(2), pages 249-282, September.
  8. Cerioli, Andrea, 2010. "Multivariate Outlier Detection With High-Breakdown Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 147-156.
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Cited by:
  1. Leonardo Grilli & Maria Iannario & Domenico Piccolo & Carla Rampichini, 2014. "Latent class CUB models," Advances in Data Analysis and Classification, Springer, vol. 8(1), pages 105-119, March.
  2. Gabriella Schoier & Adriana Monte, 2014. "On the use of cluster analysis for individuating variable influence on spread variation in large datasets," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 0(1), pages 223-229, January-M.

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