Robust Estimation in the Linear Structural Relation Model: A Study on Tuning Constants

M. M. Souto de Miranda ()
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M. M. Souto de Miranda: Universidade de Aveiro, Departamento de Matemática and U.I. & D. Matemática e Aplicações

A chapter in Developments in Robust Statistics, 2003, pp 360-367 from Springer

Abstract: Summary The parameters of a linear structural relation are unidentifiable when the errors of the model are normally distributed. For this reason the estimation of the parameters usually requires additional information and for each type of information different families of estimators were proposed; but in general they are not robust. Bounded influence estimators have been derived when the errors variance ratio is known and when instrumental variables are used. Both types of estimators depend on tuning constants, which must be chosen. The approach of fixing a priori the cut off value without knowing the population distribution has the advantage of simplifying the process. However it can introduce variability on the efficiency of the estimator, since efficiency depends on the true underlying distribution and on the form of the estimator. So, the need of objective criteria for the choice of the constant has motivated several suggestions intended for specific models. When the estimation is carried with instrumental variables, in Branco and Souto de Miranda (2000) it is suggested a method based on the influence function of the classical estimator of the relation parameters. In this study the case of known errors variance ratio is considered and the criterion based on the influence function will be adapted to the corresponding estimators.

Keywords: Instrumental Variable; Robust Estimation; Identification Case; Influence Function; Robust Estimator (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57338-5_31

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DOI: 10.1007/978-3-642-57338-5_31

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