A1000
Title: The quadratic optimization bias of large covariance matrices
Authors: Alexander Shkolnik - University of California, Santa Barbara (United States) [presenting]
Hubeyb Gurdogan - University of California, Berkeley (United States)
Abstract: The focus is on a notable puzzle involving the interactions between an optimization of a multivariate quadratic function and a plug-in estimator of a spiked covariance matrix. When the largest eigenvalues (i.e., the spikes) grow with the problem dimension, the optimized solutions inherit highly counter-intuitive properties out-of-sample. The plug-in estimator must be fine-tuned precisely or rendered virtually useless for a sufficiently large dimension. Central to the description is the quadratic optimization function, the roots of which determine this fine-tuning property. An estimator of this root is derived from a finite number of observations of a high-dimensional vector, and the consistency is proven within the high-dimensional limit. This estimator informs a low dimensional subspace correction of the sample covariance matrix when the dimension is large relative to the sample size.
