ABSTRACT
Chapters 3 to 7 mostly dealt with the methodological tools of robust estimation of location, regression and scale parameters, in univariate setups, assessing global robustness of R-estimators (shared to a certain extent by L-estimators), along with local robustness of M-estimators. Due emphasis has been laid down on their translation-scale (regression-scale) equivariance and invariance properties. The theoretical foundation of multivariate statistical estimation has been fortified by the notion of affine-equivariance and its dual affine-invariance, which are the natural generalizations of univariate translation-scale equivariance and invariance notion (Eaton 1983). This is due to the fact that multivariate parametric estimation theory has primarily evolved in the domain of elliptically symmetric distributions, which have their genesis in general multivariate normal distributions. However, general multivariate distributions, even symmetric in some sense, may not belong to the elliptically symmetric distribution family, and for which affine-equivariance (invariance) may not have a pioneering role, even under appropriate moment conditions. Also, it may not imply spherical symmetry.
