Multivariate measurement error models with normal mean‐variance mixture distributions

Abstract

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.

Likelihood‐based inference for linear mixed‐effects models using the generalized hyperbolic distribution

“…They presented an efficient EM-type algorithm for maximum likelihood (ML) estimation on the basis of the hierarchical formulation of the SMSN class. In this perspective, recent research on the topic of robust modelling suggests the use of the class of normal mean-variance mixture distributions; see for example, Barndorff-Nielsen (1997), McNeil et al (2015 and Mirfarah et al (2022) One of the most promising distributions in this class is the generalized hyperbolic (GH) distribution (Browne & McNicholas, 2015;Hellmich & Kassberger, 2011).…”