Intercept-only Model under Non-normality
Keywords:
Regression, estimation, exponential distribution, intercept-only, convergenceAbstract
In this paper, we consider a linear regression intercept-only model under the hypothesis of nonnormality. Generally, the errors are independent and normally distributed. In our case, we assume the errors are independent and follow an exponential law. We prove the consistency and establish the asymptotic distribution of the maximum likelihood estimator for the parameter of the interceptonly model. Numerical simulations confirm the accuracy of this estimator. We notably exhibit the advantages of the maximum likelihood estimator compared to the classical ordinary least square estimator. Finally, we applied the approach to a data of a real-life example, namely the Canadian lynx data.
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