Large-Scale Global and Simultaneous Inference: Estimation and Testing in Very High Dimensions
Tony Cai and Wenguang Sun
Due to advances in technology and computing, researchers are now able to collect and analyze ever large data sets. In large-scale statistical inference, we often need to solve thousands and even millions of parallel problems simultaneously; this poses many challenges and calls for new techniques. The recent two decades have seen much excitement in the statistical community to address real current needs. A plethora of detection, estimation and testing techniques have been successfully developed and applied to a wide range of data-rich fields, including financial economics, marketing analytics, social science, signal processing, and biological sciences. This article reviews significant progresses that have been made in large-scale inference, with a focus on multiple testing and false discovery rate methodologies.