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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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2012-11, Vol.18 (4), p.1284-1309
Main Authors: FASANO, MARÍA V., MARONNA, RICARDO A., SUED, MARIELA, YOHAI, VÍCTOR J.
Format: Article
Language:English
Subjects:
asymptotic normality
consistency
Consistent estimators
Estimators
Linear regression
Logical proofs
Mathematical independent variables
Mathematics
MM estimates
nonlinear regression
Point estimators
Random variables
Regression analysis
S estimates
Sufficient conditions
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Summary: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 MM-estimates are asymptotically normal when the observations are Ø-mixing.
ISSN:1350-7265
DOI:10.3150/11-BEJ368