Abstract

A large collection of statistical methods has been developed for estimation and detection of structured signals in the Gaussian and sub-Gaussian settings. In this talk, we present a general approach to robust recovery and detection of structured signals for a wide range of noise distributions. We illustrate the technique with nonparametric regression and detecting and identifying sparse short segments hidden in an ultra long linear sequence of data. A key step is the development of a quantile coupling theorem that is used to connect our problem with a more familiar Gaussian setting. An application to copy number variation (CNV) analysis based on next generation sequencing (NGS) data is also discussed.