Linear Regression with Errors not Normal: Generalized Hyperbolic Secant

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Álvaro Alexander Burbano Moreno https://orcid.org/0000-0001-8293-9705
Oscar Orlando Melo Martinez https://orcid.org/0000-0002-0296-4511

Keywords

distribution, classical linear model, modified maximum likelihood, least squares

Abstract

This paper presents a study of the model of linear regression of the type y = Θx + e, where the error has generalized hyperbolic secant distribution (GHS). The method to estimate the parameters are obtained by setting maximum likelihood expressing the non-linear equations in linear form (modified likelihood). The resulting estimators are analytical expressions in terms of values of the sample and, therefore, are easily calculables. Through the application of various types of data, the methodology described above is shown, and plausible models against the true underlying distributions of data are.

MSC: 60E05, 62E10

 

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