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Mixtures of Power Exponential Distributions and Topics in Regression-based Mixture Models

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Title: Mixtures of Power Exponential Distributions and Topics in Regression-based Mixture Models
Author: Dang, Utkarsh
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: McNicholas, Paul
Abstract: Mixture models continue to be the dominant framework for modelling heterogeneity in data. A family of mixtures of multivariate exponential power distributions that can robustly model varying tail-weight and peakedness of data is presented. A novel family of mixtures of symmetric Kotz-type distributions is also presented. In addition to modelling varying tail-weight and peakedness, this family can also account for anti-modal density shapes. Applications in model-based clustering are presented. Three types of regression-based mixture models, namely finite mixtures of regressions, finite mixtures of regression with concomitant variables, and cluster-weighted models are also extended for modelling multivariate correlated response variables in an unsupervised learning context. These models perform well on data with functional dependencies. Moreover, a family of parsimonious cluster-weighted models is presented that allows for modelling of generalized linear (binomial, Poisson, etc.) responses. Lastly, an extension of cluster-weighted models for dealing with censored competing risks data is presented via a mixture of accelerated failure time models.
URI: http://hdl.handle.net/10214/8089
Date: 2014-03
Rights: Attribution-NoDerivs 2.5 Canada
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Attribution-NoDerivs 2.5 Canada Except where otherwise noted, this item's license is described as Attribution-NoDerivs 2.5 Canada