Robust Nonparametric Inference

Abstract

In this article, we provide a personal review of the literature on nonparametric and robust tools in the standard univariate and multivariate location and scatter, as well as linear regression problems, with a special focus on sign and rank methods, their equivariance and invariance properties, and their robustness and efficiency. Beyond parametric models, the population quantities of interest are often formulated as location, scatter, skewness, kurtosis and other functionals. Some old and recent tools for model checking, dimension reduction, and subspace estimation in wide semiparametric models are discussed. We also discuss recent extensions of procedures in certain nonstandard semiparametric cases including clustered and matrix-valued data. Our personal list of important unsolved and future issues is provided.