Local statistical modeling by cluster-weighted
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arXiv:0911.2634v3 [stat.ME] 15 Jun 2011 Noname manuscript No. (will be inserted by the editor) Local Statistical Modeling via Cluster-Weighted Approach with Elliptical Distributions Salvatore Ingrassia · Simona C. Minotti · Giorgio Vittadini Received: date / Accepted: date Abstract Cluster Weighted Modeling (CWM) is a mixture approach regarding the mod- elisation of the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both the theoreti- cal 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 em- pirical studies, considering both real and simulated data. Keywords Cluster-Weighted Modeling, Mixture Models, Model-Based Clustering. Salvatore Ingrassia Dipartimento di Impresa, Culture e Societ` a Universit` a di Catania Corso Italia 55, - Catania (Italy). E-mail: [email protected] Simona C. Minotti Dipartimento di Statistica Universit` a di Milano-Bicocca Via Bicocca degli Arcimboldi 8 - 20126 Milano (Italy). E-mail: [email protected] Giorgio Vittadini Dipartimento di Metodi Quantitativi per l’Economia e le Scienze Aziendali Universit` a di Milano-Bicocca Via Bicocca degli Arcimboldi 8 - 20126 Milano (Italy). E-mail: [email protected]
Transcript of Local statistical modeling by cluster-weighted
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Noname manuscript No.(will be inserted by the editor)
Local Statistical Modeling via Cluster-Weighted Approachwith Elliptical Distributions
Salvatore Ingrassia · Simona C. Minotti · GiorgioVittadini
Received: date / Accepted: date
Abstract Cluster Weighted Modeling (CWM) is a mixture approach regarding the mod-elisation of the joint probability of data coming from a heterogeneous population. UnderGaussian assumptions, we investigate statistical properties of CWM from both the theoreti-cal and numerical point of view; in particular, we show that CWM includes as special casesmixtures of distributions and mixtures of regressions. Further, we introduce CWM based onStudent-t distributions providing more robust fitting for groups of observations with longerthan normal tails or atypical observations. Theoretical results are illustrated using some em-pirical studies, considering both real and simulated data.
Keywords Cluster-Weighted Modeling, Mixture Models, Model-Based Clustering.
Salvatore IngrassiaDipartimento di Impresa, Culture e SocietaUniversita di CataniaCorso Italia 55, - Catania (Italy). E-mail: [email protected]
Simona C. MinottiDipartimento di StatisticaUniversita di Milano-BicoccaVia Bicocca degli Arcimboldi 8 - 20126 Milano (Italy). E-mail: [email protected]
Giorgio VittadiniDipartimento di Metodi Quantitativi per l’Economia e le Scienze AziendaliUniversita di Milano-BicoccaVia Bicocca degli Arcimboldi 8 - 20126 Milano (Italy). E-mail: [email protected]
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