Calculation Method for Nonlinear Dynamic Least Absolute Deviations Estimator

概要

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In the regression models with fat tail distributions, it is well known that the Least Absolute Deviations (LAD) estimator is favorable compared with the Least Squares Estimator (LSE) because of its robustness. The LAD estimator in the linear regression model is shown its consistency and asymptotic normality, and besides linear programming method is available as calculation method. On the other hands, in the nonlinear (dynamic) model Weiss (1991) shown theoretically the consistency and asymptotic normality of the Nonlinear LAD (NLAD) estimator. But no calculation method of the NLAD estimator is proposed there. This is a critical hurdle to overcome for practical usage of the NLAD estimator. Therefore in this article, we proposed an estimator which has the same asymptotic properties as the original LAD estimator and easy to compute even in the nonlinear models, that is the generalization of Hitomi~(1997)'s Smoothed LAD (SLAD) estimator.
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