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Local Statistical Modeling via Cluster-Weighted Approach with Elliptical Distributions

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Author Info

  • Salvatore Ingrassia

    ()
    (Dipartimento di Impresa, Cultura e Società, Università degli Studi di Catania)

  • Simona Caterina Minotti

    ()
    (Dipartimento di Statistica, Università degli Studi di Milano-Bicocca)

  • Giorgio Vittadini

    ()
    (Dipartimento di Metodi Quantitativi per l'Economia e le Scienze Aziendali, Università degli Studi di Milano-Bicocca)

Abstract

Cluster Weighted Modeling (CWM) is a mixture approach regarding the modelisation of the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both the theoretical and numerical point of view; in particular, we show that CWM includes as special cases mixtures of distributions and mixtures of regressions. Further, we introduce CWM based on Student-t distributions providing more robust fitting for groups of observations with longer than normal tails or atypical observations. Theoretical results are illustrated using some empirical studies, considering both real and simulated data.

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File URL: http://www.statistica.unimib.it/utenti/WorkingPapers/WorkingPapers/20111001.pdf
File Function: Third version, 2011
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Bibliographic Info

Paper provided by Università degli Studi di Milano-Bicocca, Dipartimento di Statistica in its series Working Papers with number 20111001.

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Length: 30 pages
Date of creation: 28 May 2011
Date of revision:
Handle: RePEc:mis:wpaper:20111001

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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. 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.
  4. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer, vol. 5(2), pages 249-282, September.
  5. 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.
  6. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer, vol. 12(1), pages 21-55, March.
  7. 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.
  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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