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Título: Robust estimation in a multivariate normal regression model with general parameterization.
Resumo: This work explores the use of a non-extensive q-entropy measure for parameter estimation in a multivariate normal regression model with general parameterization. This model encompasses a large class of regression models that includes mixed models, errors-in-variables models, nonlinear models, among others. The resulting estimator, called the maximum L_q-likelihood estimator, depends on a tuning parameter q that is chosen to improve inferential accuracy in the presence of outliers. We derive the quantities required to obtain the parameter estimates and the asymptotic variance and covariance matrix of the maximum L_q-likelihood estimator under this general class of models. Some of these quantities are explained in detail for three specific cases, namely, mixed models, errors-in-variables models, and nonlinear models. Although the maximum L_q-likelihood estimator may not be consistent, we obtain a new estimator that satisfies this property through a calibration function.
Additionally, we also obtain another robust and consistent estimator that minimizes an empirical version of the density power divergence, called the minimum density power divergence estimator.
To evaluate the performance of our proposal, we conduct Monte Carlo simulations in the absence and presence of outliers under finite samples. Finally, we apply our method to actual data.