Multivariate Analysis and Random Matrices in Statistics

Random matrices arise frequently in modern statistical theory, and tools reflecting their properties are the basis of many statistical tests and estimation procedures. Random Matrix theory is both an appealing branch of pure mathematics and an important engine for understanding many phenomena that appear in dealing with modern high-dimensional data. We will emphasize (a) phenomena - the strange things that can happen in high dimensions; (b) sightings - places where these phenomena appear and help explain puzzles in modern machine learning and statistics; (c) monuments - the central objects in the mathematical theory, their names and properties; (d) applications - ways that RMT helps statisticians and applied mathematicians in modern research. We will discuss Sparse principal component analysis (Sparse PCA) as well as Johnstone, Generalized and Canonical Correlation Spiked Models.