Continuity and differentiability of regression M functionals

FASANO MARÍA VICTORIA; MARONNA, RICARDO ANTONIO; SUED MARIELA; YOHAI VÍCTOR

BERNOULLI - MATHEMATICAL STATISTICS AND PROBABILITY

INT STATISTICAL INST

Lugar: Amsterdam; Año: 2011

1350-7265

This paper deals with the Fisher?consistency, weak continuity and di¤erentiability 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 di¤erentiability, called weak di¤erentiability, is de?ned, which su¢ ces 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 -mixing.