Continuity and differentiability of regression M-estimates

Details Continuity and differentiability of regression M-estimates Continuity and differentiability of regression M-estimates

2010-04-24

arxiv.org/abs/1004.4314v2

Mathematics

Statistics Theory

Scientific paper

This paper deals with the weak continuity, Fisher-consistency 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 estimates under more general conditions than those required in standard approaches.

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