Robust Statistics for High-dimensional Data

Modern data analysis is frequently involved with high-dimensional data sets. High-dimensionality means that the sample length, n, is smaller or not much larger than the dimension, p, of the data set where p is very large (often tens of thousands or larger). This implies that the number of covariates in regression model can exceed the number of observations, a regime opposite to conventional statistical settings. Data-sets with large number of variables but relatively small sample size pose great unprecedented challenges and opportunities for statistical analysis. The goal of this project is to develop new advanced robust multivariate statistical analysis methods for high-dimensional data. In particular, new methods for robust estimation of high-dimensional covariance matrices and sparse structured multivariate regression are developed. Scalable and distributed robust statistical inference procedures based on bootstrap are developed as well.