On Extreme Value Asymptotics of Projected Sample Covariances in High Dimensions with Applications in Finance and Convolutional Networks

Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a dataset has been collected under normal conditions. Within a linear time series framework, it is shown that Gumbel-type extreme value asymptotics hold true. As applications, we discuss long-only mimimal-variance portfolio optimization, ETF index tracking, convolutional deep learners for image analysis, and the analysis of array-of-sensors data.