Robust mixture modeling based on scale mixtures of skew-normal distributions

Basso, Rodrigo Marreiro; Lachos, Víctor H.; Cabral, Celso Rômulo Barbosa; Ghosh, Pulak

doi:10.1016/j.csda.2009.09.031

Cited by 135 publications

(110 citation statements)

References 24 publications

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“…In this section, we study the VB non-linear regression model using a similar approach to that used by Lachos et al (2011), Labra et al (2012 and Basso et al (2010). Specifically, we consider the non-linear regression model (2) with the assumption that the random errors ε t are independent, heteroscedastic and distributed throughout SMSN class of distributions.…”

Section: Methodsmentioning

confidence: 99%

“…The first and second derivatives of t (θ) are given in Basso et al (2010) for arbitrary specifications of η t and σ 2 t . From these results we can obtain the observed information matrix, namely…”

Section: The Skew-t Special Casementioning

confidence: 99%

“…Specifically, as in Basso et al (2010), we consider the class of scale mixture of the skew-normal (SMSN) distributions (Branco & Dey, 2001) for random errors. The SMSN is an attractive class of asymmetric heavy-tailed distributions that are useful for robust inference when the normality assumption for error distribution is unrealistic.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

Contreras-Reyes

Arellano–Valle²

2013

Fisheries Research

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Our article presents a robust and flexible statistical modeling for the growth curve associated to the age-length relationship of Cardinalfish (Epigonus Crassicaudus). Specifically, we consider a non-linear regression model, in which the error distribution allows heteroscedasticity and belongs to the family of scale mixture of the skewnormal (SMSN) distributions, thus eliminating the need to transform the dependent variable into many data sets. The SMSN is a tractable and flexible class of asymmetric heavy-tailed distributions that are useful for robust inference when the normality assumption for error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew-t distributions. In this work emphasis is given to the skew-t model. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by previous analysis about of Cardinalfish age, in which a maximum age of 15 years has been determined. Therefore, in this study we carry out the mentioned methodology over a data set that include a long-range of ages based on an otolith sample where the determined longevity is higher than 54 years.

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Section: Methodsmentioning

confidence: 99%

Section: The Skew-t Special Casementioning

confidence: 99%

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Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

Contreras-Reyes

Arellano–Valle²

2013

Fisheries Research

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“…Even though the new model has a heavy tail the FM-T model cannot be ideal in the presence of highly asymmetric observations. To produce a flexible model with wider ranges of skewness and kurtosis, Basso et al (2010) studied a class of mixture models where the component densities are scale mixtures of the (univariate) skew-normal distributions, which include skew-normal, skew-t, skewcontaminated normal and skew-slash distributions as special cases. Following their work, Cabral et al (2012) introduced the finite mixture of multivariate scale mixtures of the skew-normal distributions and studied its properties.…”

Section: Introductionmentioning

confidence: 99%

On the Finite Mixture Modelling via Normal Mean-variance Birnbaum-Saunders Distribution

Naderi¹,

Arabpour²,

Jamalizadeh³

2017

JIRSS

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Abstract. This paper presents a new finite mixture model using the normal meanvariance mixture of Birnbaum-Saunders distribution. The proposed model is multimodal with wider ranges of skewness and kurtosis. Moreover, it is useful for modeling highly asymmetric data in various theoretical and applied statistical problems. The maximum likelihood estimates of the parameters of the model are computed iteratively by feasible EM algorithm. To illustrate the finite sample properties and performance of the estimators, we conduct a simulation study and illustrate the usefulness of the new model by analyzing a real dataset.

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“…Alcantara and Cysneiros (2017) used slash-elliptical distribution for error term in NLM and estimate its parameters by the maximum likelihood method. Such classes of distributions contain skewed versions of classical distributions such as skew-normal, skew-t, skew-slash (Gomez and Venegas, 2008) and skew contaminated normal distribution (Basso et al, 2010). Lachos et al (2011) defined scale mixtures of skew-normal heteroscedastic NLM and estimate its parameters by applying an EM-type algorithm.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Regression Models Based on Slash Skew-elliptical‎ ‎Errors

Nahooji

Farnoosh

Nematollahi

2018

JIRSS

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Abstract. In this paper, the nonlinear regression models when the model errors follow a slash skew-elliptical distribution, are considered. In the special case of nonlinear regression models under slash skew-t distribution, we present some distributional properties, and to estimate their parameters, we use an EM-type algorithm. Also, to find the estimation errors, we derive the observed information matrix analytically. To describe the influence of the observations on the ML estimates, we use a sensitivity analysis. Finally, we conduct some simulation studies and a real data analysis to show the performance of the proposed model.

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Robust mixture modeling based on scale mixtures of skew-normal distributions

Cited by 135 publications

References 24 publications

Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

On the Finite Mixture Modelling via Normal Mean-variance Birnbaum-Saunders Distribution

Nonlinear Regression Models Based on Slash Skew-elliptical‎ ‎Errors

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