Mehmet Caner Agostino Capponi Mihailo Stojnic
arXiv 7 Jul 2025 · Econometrics
arXiv:2507.04663 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bing, X., F. Bunea, S. Strimas-Mackey, and M. Wegkamp (2021) Prediction under latent factor regression: adaptive pcr, interpolating predictors and beyond | 1.000 | 26 | 5 | 100% |
| 2 | Bunea, F., S. Strimas-Mackey, and M. Wegkamp (2022) Interpolating predictors in high dimensional factor estimation | 1.000 | 23 | 5 | 100% |
| 3 | Callot, L., M. Caner, O. Onder, and E. Ulasan (2021) A nodewise regression approach to estimating large portfolios | 1.000 | 8 | 4 | 100% |
| 4 | Caner, M., M. Medeiros, and G. Vasconcelos (2023) Sharpe ratio analysis in high dimensions: Residual based nodewise regression in factor models | 1.000 | 8 | 3 | 100% |
| 5 | Fan, J., Y. Liao, and M. Mincheva (2013) Large covariance estimation by thresholding principal orthogonal complements | 1.000 | 6 | 3 | 100% |
| 6 | Ledoit, O, M. and M. Wolf (2017) Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets goldilocks | 0.928 | 4 | 3 | 100% |
| 7 | Meinshausen, N. and P. Bühlmann (2006) High-dimensional graphs and variable selection with the lasso | 0.737 | 3 | 2 | 100% |
| 8 | Vershynin, R (2019) High Dimensional Probability: An Introduction with Applications in Data Science | 0.693 | 10 | 1 | 100% |
| 9 | Abadir, K. and J. Magnus (2005) Matrix Algebra | 0.693 | 6 | 1 | 100% |
| 10 | Bernstein, D (2018) Scalar vector, and matrix mathematics, theory facts and formulas | 0.644 | 4 | 1 | 100% |
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