A two-piece normal measurement error model

The mixture‐of‐experts (MoE) paradigm attempts to learn complex models by combining several “experts” via probabilistic mixture models. Each expert in the MoE model handles a small area of the data space in which a gating function controls the data‐to‐expert assignment. The MoE framework has been used extensively in designing non‐linear models in machine learning and statistics to model the heterogeneity in data for the purpose of regression, classification and clustering. The existing MoE of multi‐target regression (MoE‐MTR) models for continuous data is based on multivariate normal distributions. However, in many practical situations, for a set of data, a group or groups of observations may exhibit asymmetric and heavy‐tailed behaviour, and inference based on symmetric distributions in such situations can unduly affect the fit of the regression model. We introduce here a novel robust multivariate non‐normal MoE model by the use of mean mixture of normal distributions. The proposed model can handle the issues of MoE‐MTR models regarding possibly skewed, heavy‐tailed and noisy data. Maximum likelihood estimates of model parameters are developed based on an expectation‐maximization (EM)‐type algorithm. Parsimony is also obtained by imposing suitable constraints on the expert dispersion matrices. The usefulness of the proposed methodology is illustrated using simulated and real data sets.

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“…where I A (Á) denotes the indicator function of set A; see Arellano-Valle et al (2020). The mean and variance of W are given by…”

Section: Special Cases Of Mmmn Distributionsmentioning

confidence: 99%

“…To obtain the estimate of η j for the MoE-MTR TPrSN model, the following technical procedure can be followed. Arellano-Valle et al (2020) showed that the random variable W in (6) can be generated as W ¼ UR, where R $ TNð0, 1;ð0, ∞ÞÞ and independently of U $ Pðu;…”

Section: Parameter Estimationmentioning

confidence: 99%

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

Sepahdar

Madadi

Jamalizadeh

2022

Stat

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“…Expressions of the score functions of the (profile) log-likelihood and other results useful for maximum likelihood estimation (MLE) are provided by Azzalini and Capitanio [11] for the SN case, and by Azzalini and Capitanio [19] for the ST case. Multivariate measurement error models have been considered by Lachos et al [71] and by Arellano-Valle et al [72].…”

Section: Regression Models and Variantsmentioning

confidence: 99%

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

Adcock

Azzalini

2020

Symmetry

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Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skew-elliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to non-specialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required.

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“…Later on, Lachos et al (2009Lachos et al ( , 2010 proposed a robust extension of the MEMs by considering a class of asymmetric thick-tailed distributions, including the skew-normal/independent and scale mixtures of the skew-normal distributions. More recently, Arellano-Valle et al (2020) defined a novel MEM based on the two-piece normal distribution that acts as an alternative model for accommodating asymmetrical features.…”

Section: Introductionmentioning

confidence: 99%

Multivariate measurement error models with normal mean‐variance mixture distributions

Mirfarah

Naderi

Lin

et al. 2022

Stat

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The class of normal mean‐variance mixture (NMVM) distributions is a rich family of asymmetric and heavy‐tailed distributions and has been widely considered in parametric modeling of the data for robust statistical inference. This paper proposes an extension of measurement error models by assuming the NMVM distributions for the unobserved covariates and error terms in the model, referred to as the NMVM‐MEM. An expectation conditional maximization either (ECME) algorithm is developed to compute the maximum likelihood (ML) estimates of model parameters. Furthermore, an information‐based approach is performed to derive the asymptotic covariance matrix of ML estimators. The analysis of a blood pressure dataset illustrates the superiority of NMVM‐MEM to accommodate asymmetry and outliers over the normal counterpart. Two simulation studies are undertaken to validate our proposed techniques.

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A two-piece normal measurement error model

Cited by 9 publications

References 26 publications

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

Multivariate measurement error models with normal mean‐variance mixture distributions

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