Title: Shrinking characteristics of precision matrix estimators
Abstract: We propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative log-likelihood plus an L1 penalty on a linear function evaluated at the optimization variable corresponding to the precision matrix. We establish convergence rate bounds for these estimators and we propose an alternating direction method of multipliers algorithm for their computation. Our simulation studies show that our estimators can perform better than competitors when they are used to fit predictive models. In particular, we illustrate cases where our precision matrix estimators perform worse at estimating the population precision matrix while performing better at prediction. This is joint work with Aaron Molstad.