Inference in Multiple Linear Regression Model with Generalized Secant Hyperbolic Distribution Errors

Main Article Content

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

Keywords

Maximum likelihood, Modified maximum likelihood, Least square, Generalized Secant Hyperbolic distribution, Robustness, Hypothesis testing

Abstract

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. We derive the estimators of model parameters by using
modified maximum likelihood methodology and explore the properties of the modified maximum likelihood estimators so obtained. We show that the proposed estimators are more efficient and robust than the commonly used least square estimators. We also develop the relevant test of hypothesis procedures and compared the performance of such tests vis-a-vis the classical tests that are based upon the least square approach. 

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