Locally robust methods and near-parametric asymptotics

It has already been shown theoretically and numerically that infusing a little localization in the likelihood-based methods for regression and for density estimation can actually improve the resulting estimators with respect to suitably defined global risk measures. Thus various local likelihood methods have been suggested. In this paper, we demonstrate that a similar effect can also be observed with respect to robust estimation procedures. Localized versions of robust density estimation procedures perform better with respect to global risk measures based on minimization of Bregman divergence measures.