SOME PRACTICAL CONSIDERATIONS ABOUT PRECISION OF ESTIMATORS OF MINIMUM SQUARES AND LIKELIHOOD FOR THE PARAMETERS OF LINEAR REGRESSION NORMAL
Keywords:Estimador de mínimos quadrados, Estimador de máxima verossimilhança, regressão linear, precisão
In this paper, we discuss some practical considerations on the use of different methods for the estimation of linear regression parameters and their impact on the obtained inferences. In practice, it is common to use some existing statistical software to obtain the least squares estimators (MSE) for the regression parameters and consider a non-biased estimator for the variance based on the residual squared sum of the residuals. Alternatively, we discuss the use of the maximum likelihood estimator (MLE) for the variance of the error (an unbiased estimator, but with smaller squared error) which may lead to different conclusions in terms of inferences. Two numerical examples are presented to illustrate the proposed method.
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