Continuity and differentiability of regression M functionals
This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A restricted type of differentiability, called weak differenti...
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2012
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13507265_v18_n4_p1284_Fasano http://hdl.handle.net/20.500.12110/paper_13507265_v18_n4_p1284_Fasano |
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| Sumario: | This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A restricted type of differentiability, called weak differentiability, is defined, which suffices to prove the asymptotic normality of estimates based on the functionals. This approach allows to prove the consistency, asymptotic normality and qualitative robustness of M estimates under more general conditions than those required in standard approaches. In particular, we prove that regression MMestimates are asymptotically normal when the observations are φ-mixing. © 2012 ISI/BS. |
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