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A note on the Gao et al. (2019) uniform mixture model in the case of regression

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<mark>Journal publication date</mark>1/06/2020
<mark>Journal</mark>Annals of Operations Research
Volume289
Number of pages7
Pages (from-to)495–501
Publication StatusPublished
Early online date21/11/19
<mark>Original language</mark>English

Abstract

We extend the uniform mixture model of Gao et al. (Ann Oper Res, 2019. https://doi.org/10.1007/s10479-019-03236-9) to the case of linear regression. Gao et al. (Ann Oper Res, 2019. https://doi.org/10.1007/s10479-019-03236-9) proposed that to characterize the probability distributions of multimodal and irregular data observed in engineering, a uniform mixture model can be used. This model is a weighted combination of multiple uniform distribution components. This case is of empirical interest since, in many instances, the distribution of the error term in a linear regression model cannot be assumed unimodal. Bayesian methods of inference organized around Markov chain Monte Carlo are proposed. In a Monte Carlo experiment, significant efficiency gains are found in comparison to least squares justifying the use of the uniform mixture model.