A General Class of Model-Free Dense Precision Matrix Estimators

• URL: http://arxiv.org/abs/2507.04663v1
• Date: Mon, 07 Jul 2025 05:07:17 GMT
• Title: A General Class of Model-Free Dense Precision Matrix Estimators
• Abstract summary: We introduce prototype consistent model-free, dense precision matrix estimators that have broad application in economics.<n>We are able to: (i) obtain non-asymptotic bounds for precision matrix estimation errors; (ii) uncover the existence of an intrinsic signal-to-noise; and (iv) avoid exact population sparsity assumptions.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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