Multivariate linear regression with non-normal errors: a solution based on mixture models

Soffritti, Gabriele; Galimberti, Giuliano

doi:10.1007/s11222-010-9190-3

Cited by 31 publications

(35 citation statements)

References 50 publications

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“…The Australian Institute of Sports (AIS) data (Cook and Weisberg, 1994) contains measurements on 202 athletes (100 female and 102 male) and is available in the R package sn (Azzalini, 2013). A subset of seven variables that has recently been used in the mixtures of regression literature (Soffritti and Galimberti, 2011) is analyzed here: red cell count (RCC), white cell count (WCC), plasma ferritin concentration (PFC), body mass index, sum of skin folds, body fat percentage, and lean body mass. The blood composition variables (RCC, WCC, and PFC) are selected as the response variables with the biometrical variables being the predictors.…”

Section: Australian Institute Of Sports Datamentioning

confidence: 99%

Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models

et al. 2017

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A family of parsimonious Gaussian cluster-weighted models is presented. This family concerns a multivariate extension to cluster-weighted modelling that can account for correlations between multivariate responses. Parsimony is attained by constraining parts of an eigendecomposition imposed on the component covariance matrices. A sufficient condition for identifiability is provided and an expectation-maximization algorithm is presented for parameter estimation. Model performance is investigated on both synthetic and classical real data sets and compared with some popular approaches. Finally, accounting for linear dependencies in the presence of a linear regression structure is shown to offer better performance, vis-à-vis clustering, over existing methodologies.

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Section: Australian Institute Of Sports Datamentioning

confidence: 99%

Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models

et al. 2017

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“…Liu and Bozdogan [21] studied on multivariate regression models with PE random errors under various assumptions. Soffritti and Galimberti [22] discussed a multivariate linear regression model under the assumption that the error terms follow a finite mixture of normal distributions. Jafari and Hashemi [23] studied on linear regression with the error term of skewnormal distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation of a linear model with two-parameter symmetric platykurtic distributed errors

Andargie

Rao

2013

J. Uncertain. Anal. Appl.

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Purpose: A linear regression model with Gaussian-distributed error terms is the most widely used method to describe the possible relationship between outcome and predictor variables. However, there are some drawbacks of Gaussian errors such as the distribution being mesokurtic. In many practical situations, the variables under study may not be mesokurtic but are platykurtic. Hence, to analyze this sort of platykurtic variables, a multiple regression model with symmetric platykurtic (SP) distributed errors is needed. In this paper, we introduce and develop a multiple linear regression model with symmetric platykurtic distributed errors for the first time.Methods: We used the methods of ordinary least squares (OLS) and maximum likelihood (ML) to estimate the model parameters. The properties of the ML estimators with respect to the symmetric platykurtic distributed errors are discussed. The model selection criteria such as Akaike information criteria (AIC) and Bayesian information criteria (BIC) for the models are used. The utility of the proposed model is demonstrated with both simulation and real-time data.Results: A comparative study of symmetric platykurtic linear regression model with the Gaussian model revealed that the former gives good fit to some data sets. The results also revealed that ML estimators are more efficient than OLS estimators in terms of the relative efficiency of the one-step-ahead forecast mean square error. Conclusions: The study shows that the symmetric platykurtic distribution serves as an alternative to the normal distribution. The developed model is useful for analyzing data sets arising from agricultural experiments, portfolio management, space experiments, and a wide range of other practical problems.

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“…The proposed methods can be extended to multivariate settings using the multivariate SMSN class of distributions (Cabral et al, 2012), such as the recent proposals of Soffritti and Galimberti (2011) and Galimberti and Soffritti (2014). Due to the popularity of Markov chain Monte Carlo techniques, another potential work is to pursue a fully Bayesian treatment in this context for producing posterior inference.…”

Section: Discussionmentioning

confidence: 99%

“…1. To extend the estimation results obtained in the model presented in the first paper (FM-SMSN-LR) where the error follows a finite mixture of a multivariate of SMSN distributions, inspired by the works of Soffritti and Galimberti (2011) and Galimberti and Soffritti (2014).…”

Section: Suggestions For Future Researchmentioning

confidence: 99%

“…To overcome these problems, solutions that use finite mixture (FM-LR) models have been recently proposed. For instance, Bartolucci and Scaccia (2005), Soffritti and Galimberti (2011) and Galimberti e Soffritti (2014) have developed methods for linear regression analysis by assuming a finite mixture of Gaussian (FM-N-LR) and Student-t (FM-T-LR) components for the error terms.…”

Section: Introductionmentioning

confidence: 99%

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Finite mixture of regression models

Sánchez¹

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This dissertation consists of three articles, proposing extensions of finite mixtures in regression models. Here we consider a flexible class of both univariate and multivariate distributions, which allow adequate modeling of asymmetric data that have multimodality, heavy tails and outlying observations. This class has special cases such as skew-normal, skew-t, skew-slash and skew normal contaminated distributions, as well as symmetric cases. Initially, a model is proposed based on the assumption that the errors follow a finite mixture of scale mixture of skew-normal (FM-SMSN) distribution rather than the conventional normal distribution. Next, we have a censored regression model where we consider that the error follows a finite mixture of scale mixture of normal (SMN) distribution. Next, we propose a censored regression model where we consider that the error follows a finite mixture of scale mixture of normal (SMN) distribution. Finally, we consider a finite mixture of multivariate regression where the error has a multivariate SMSN distribution. For all proposed models, two R packages were developed, which are reported in the appendix.

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Multivariate linear regression with non-normal errors: a solution based on mixture models

Cited by 31 publications

References 50 publications

Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models

Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models

Estimation of a linear model with two-parameter symmetric platykurtic distributed errors

Finite mixture of regression models

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