A two-piece normal measurement error model

Reinaldo B. Arellano-Valle, Adelchi Azzalini, Clécio S. Ferreira and Karol Santoro

Computational Statistics & Data Analysis, 2020, vol. 144, issue C

Abstract: In the context of measurement error models, the true unobservable covariates are commonly assumed to have a normal distribution. This assumption is replaced here by a more flexible two-piece normal distribution, which allows for asymmetry. After setting-up a general formulation for two-piece distributions, we focus on the case of the normal two-piece construction. It turns out that the joint distribution of the actual observations (the multivariate observed covariates and the response) is a two-component mixture of multivariate skew-normal distributions. This connection facilitates the construction of an EM-type algorithm for performing maximum likelihood estimation. Some numerical experimentation with two real datasets indicates a substantial improvement of the present formulation with respect to the classical normal-theory construction, which greatly compensates the introduction of a single parameter for regulation of skewness.

Keywords: Two-piece distributions; Two-piece normal distribution; Multivariate skew-normal distribution; Measurement error model; ECM algorithm (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:144:y:2020:i:c:s016794731930218x

DOI: 10.1016/j.csda.2019.106863

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