Weak Continuity and Differentiability of Regression M Estimating Functionals
ABSTRACT
This talk 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 alpha-mixing.
This is a joint work with María V. Fasano (Universidad Nacional de La Plata), Ricardo A.Maronna (Universidad Nacional de La Plata), Mariela Sued (Universidad de Buenos Aires and CONICET) and Víctor J. Yohai (Universidad de Buenos Aires and CONICET)
|