Short Course - Robust Statistical Inference for High-Dimensional Data

This course will provide an overview of the parametric statistical procedures for high-dimensional data, focusing primarily on the robustness aspects against data contamination. Our main consideration would be the problem of simultaneous variable selection and parameter estimation under the high-dimensional regression set-ups, both under the high-dimensional linear and generalized linear models (GLMs).

We will first start with the discussions on the needs of appropriate robust statistical methodologies for deriving stable and correct inferences from noisy high-dimensional data. A brief review of the existing methods for robust and sparse estimation will be covered, with the details for the two major classes of such procedures, namely the class of penalized M-estimators and the regularized minimum divergence estimators with particular emphasis on the density power divergence.

The oracle consistency and asymptotic normality of these robust estimators will be discussed under appropriate conditions. In the final part of the course, several practical aspects of these procedures will be dicussed, particularly covering the robust and adaptive procedures to reduce the number of false discoveries and robust variable screening for ultra-high dimensional data in real-life applications.