Locally and globally robust estimators in regression

Sonia Hernández and Víctor J. Yohai

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: A new class of estimates for the linear model is introduced. These estimators, that we eaU C-estimators, are defined as a linear convex combination of the Rousseeuw's least median squares (LMS-) estimator and any other estimate, T2• We prove that C-estimators retain the high breakdown point of the LMS-estimator, but inherit the asymptotic properties and the behaviour in terms of local robutness of T2• In particular, a Cestimators will have --In-asymptotics and bounded contamination sensitivity if T2 does. In addition, efficiency, local robustness properties and the maximum bias curve of C-estimators are investigated for different choices ofT2•

Keywords: Linear; regression; robust; estimates; maximum; bias; function; high; breakdown; point; contamination; sensivity; high; efficiency (search for similar items in EconPapers)
Date: 1999-07
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:6348

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