Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling (original) (raw)

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

TEST, 2015

The traditional estimation of mixture regression models is based on the assumption of normality (symmetry) of component errors and thus is sensitive to outliers, heavy-tailed errors and/or asymmetric errors. In this work we present a proposal to deal with these issues simultaneously in the context of the mixture regression by extending the classic normal model by assuming that the random errors follow a scale mixtures of skew-normal distributions. This approach allows us to model data with great flexibility, accommodating skewness and heavy tails. The main virtue of considering the mixture regression models under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows easy implementation of inference. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters of the proposed model. In order to examine the robust aspect of this flexible model against outlying observations, some simulation studies are also been presented. Finally, a real data set is analyzed, illustrating the usefulness of the proposed method.

Heteroscedastic and heavy-tailed regression with mixtures of skew Laplace normal distributions

Journal of Statistical Computation and Simulation

Joint modelling skewness and heterogeneity is challenging in data analysis, particularly in regression analysis which allows a random probability distribution to change flexibly with covariates. This paper, based on a skew Laplace normal (SLN) mixture of location, scale, and skewness, introduces a new regression model which provides a flexible modelling of location, scale and skewness parameters simultaneously. The maximum likelihood (ML) estimators of all parameters of the proposed model via the expectation-maximization (EM) algorithm as well as their asymptotic properties are derived. Numerical analyses via a simulation study and a real data example are used to illustrate the performance of the proposed model.

Multivariate mixture modeling using skew-normal independent distributions

2012

In this paper we consider a flexible class of models, with elements that are finite mixtures of multivariate skew-normal independent distributions. A general EM-type algorithm is employed for iteratively computing parameter estimates and this is discussed with emphasis on finite mixtures of skew-normal, skew-t, skew-slash and skew-contaminated normal distributions. Further, a general information-based method for approximating the asymptotic covariance matrix of the estimates is also presented. The accuracy of the associated estimates and the efficiency of some information criteria are evaluated via simulation studies. Results obtained from the analysis of artificial and real data sets are reported illustrating the usefulness of the proposed methodology. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn.

Robust mixture regression based on the skew t distribution

Revista Colombiana de Estadística, 2017

In this study, we propose a robust mixture regression procedure based on the skew t distribution to model heavy-tailed and/or skewed errors in a mixture regression setting. Using the scale mixture representation of the skew t distribution, we give an Expectation Maximization (EM) algorithm to compute the maximum likelihood (ML) estimates for the paramaters of interest. The performance of proposed estimators is demonstrated by a simulation study and a real data example.

Skew scale mixtures of normal distributions: Properties and estimation

Statistical Methodology, 2011

Scale mixture of normal distributions are often used as a challenging family for statistical procedures of symmetrical data. In this article, we have defined a skewed version of these distributions and we have derived several of its probabilistic and inferential properties. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine EM algorithms for maximum likelihood estimation. For univariate skewed responses, the EM-type algorithm has been discussed with emphasis on the skew-t, skew-slash, skew-contaminated normal and skew-exponential power distributions. Some simplifying and unifying results are also noted with the Fisher informating matrix, which is derived in closed form for some distributions in the family. Results obtained from simulated and real data sets are reported illustrating the usefulness of the proposed methodology. The main conclusion in reanalyzing a data set previously studied is that the models so far entertained are clearly not the most adequate ones.

Finite mixture modeling using shape mixtures of the skew scale mixtures of normal distributions

2020

This paper introduces the shape mixtures of the skew scale mixtures of normal distribution which are contained additional shape parameters to regulate skewness and kurtosis. We present a finite mixture model for this new family of distributions, which is a novel model-based tool for clustering heterogeneous data in the presence of skewed and heavy-tailed outcomes. The maximum likelihood estimates of the parameters of the proposed models are obtained by developing an Expectation Conditional Maximization Either algorithm. The numerical performance of the proposed methodology is illustrated through simulated and real data examples.

A New Extended Mixture Skew Normal Distribution, With Applications

Revista Colombiana de Estadística

One of the most important property of the mixture normal distributions-model is its flexibility to accommodate various types of distribution functions (df's). We show that the mixture of the skew normal distribution and its reverse, after adding a location parameter to the skew normal distribution, and adding the same location parameter with different sign to its reverse is a family of df's that contains all the possible types of df's. Besides, it has a very remarkable wide range of the indices of skewness and kurtosis. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates of the model parameters. Moreover, an application with a body mass index real data set is presented.

Finite Mixtures of Multivariate Skew Laplace Distributions

arXiv: Statistics Theory, 2017

In this paper, we propose finite mixtures of multivariate skew Laplace distributions to model both skewness and heavy-tailedness in the heterogeneous data sets. The maximum likelihood estimators for the parameters of interest are obtained by using the EM algorithm. We give a small simulation study and a real data example to illustrate the performance of the proposed mixture model.

Finite mixtures of skew Laplace normal distributions with random skewness

Computational Statistics, 2020

In this paper, the shape mixtures of the skew Laplace normal (SMSLN) distribution is introduced as a flexible extension of the skew Laplace normal distribution which is also a heavy-tailed distribution. The SMSLN distribution includes an extra shape parameter, which controls skewness and kurtosis. Some distributional properties of this distribution are derived. Besides, we propose finite mixtures of SMSLN distributions to model both skewness and heavy-tailedness in heterogeneous data sets. The maximum likelihood estimators for parameters of interests are obtained via the expectation-maximization algorithm. We also give a simulation study and examine a real data example for the numerical illustration of proposed estimators.

On mixtures of skew normal and skew t$$ -distributions

Advances in Data Analysis and Classification, 2013

Finite mixtures of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the connections between them and their relative performance becomes rather unclear. This paper aims to provide a concise overview of these developments by presenting a systematic classification of the existing skew symmetric distributions into four types, thereby clarifying their close relationships. This also aids in understanding the link between some of the proposed expectation-maximization (EM) based algorithms for the computation of the maximum likelihood estimates of the parameters of the models. The final part of this paper presents an illustration of the performance of these mixture models in clustering a real dataset, relative to other non-elliptically contoured clustering methods and associated algorithms for their implementation.