A robust multivariate measurement error model with skew-normal/independent distributions and Bayesian MCMC implementation

Lachos, Víctor H.; Garibay, Victoria M.; Labra, Filidor V.; Aoki, Reiko

doi:10.1016/j.stamet.2009.06.002

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…Compared to the EM‐type algorithm, utilizing Bayesian methods can also simplify the parameter estimation procedure, especially when the conditional expectations do not exist. Therefore, a possible research direction is to investigate a fully Bayesian treatment via exploring Markov Chain Monte Carlo procedures, such as the Gibbs sampler and the Metropolis‐Hastings algorithm (Arellano‐Valle et al, 2005; Lachos et al, 2009). Analyzing censored data has unceasingly been encountered in diverse scientific fields such as econometrics, biometrics, and clinical trials.…”

Section: Discussionmentioning

confidence: 99%

“…Bolfarine and Lachos (2006) extended structural probit measurement error models by assuming the skew-normal distribution on the unobserved covariates for analyzing data with binary response variables. 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%

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Multivariate measurement error models with normal mean‐variance mixture distributions

Mirfarah

Naderi

Lin

et al. 2022

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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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Section: Discussionmentioning

confidence: 99%