Multivariate measurement error models for replicated data under heavy‐tailed distributions

Abstract

In this paper, we deal with multivariate measurement error models for replicated data under heavy‐tailed distributions, providing appealing robust and adaptable alternatives to the usual Gaussian assumptions. The models contain both error‐prone covariates and predictors measured without errors. The surrogates of the response and the multiple error‐prone covariates are replicated and are allowed unpaired and/or unequal cases. Under the scale mixtures of normal distribution class, we provide an explicit iterative formula of the maximum likelihood estimation via an expectation‐maximization‐type algorithm. Closed forms of asymptotic variances of the estimators are also given. The effect and robustness performances are confirmed by the simulation studies. Two real data sets are analyzed by the proposed models. Copyright © 2015 John Wiley & Sons, Ltd.