A General Class of Model-Free Dense Precision Matrix Estimators

We introduce prototype consistent model-free, dense precision matrix estimators that have broad application in economics. Using quadratic form concentration inequalities and novel algebraic characterizations of confounding dimension reductions, we are able to: (i) obtain non-asymptotic bounds for precision matrix estimation errors and also (ii) consistency in high dimensions; (iii) uncover the existence of an intrinsic signal-to-noise -- underlying dimensions tradeoff; and (iv) avoid exact population sparsity assumptions. In addition to its desirable theoretical properties, a thorough empirical study of the S&P 500 index shows that a tuning parameter-free special case of our general estimator exhibits a doubly ascending Sharpe Ratio pattern, thereby establishing a link with the famous double descent phenomenon dominantly present in recent statistical and machine learning literature.