{"ID":2897344,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.04663","arxiv_id":"2507.04663","title":"Model-Estimation-Free, Dense, and High Dimensional Consistent Precision Matrix Estimators","abstract":"Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While each of these targets can be met separately, achieving them together is challenging.We address this gap by introducing a general class of estimators that unifies these features within a nonasymptotic framework, allowing for explicit characterization of the computational complexity, signal-to-noise ratio trade-off. Our analysis identifies three fundamental random quantities, complexity, signal magnitude, and method bias that jointly determine estimation error. A particularly striking result is that ridgeless regression, a tuning-free special case within our class, exhibits the double descent phenomenon. This establishes the first formal precision matrix analogue to the well-known double descent behavior in linear regression. Our theoretical analysis is supported by a thorough empirical study of the S\\\u0026P 500 index, where we observe a doubly ascending Sharpe ratio pattern, which complements the double descent phenomenon.","short_abstract":"Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While each of these targets can be met separately, achieving them together is challenging...","url_abs":"https://arxiv.org/abs/2507.04663","url_pdf":"https://arxiv.org/pdf/2507.04663v2","authors":"[\"Mehmet Caner Agostino Capponi Mihailo Stojnic\"]","published":"2025-07-07T05:07:17Z","proceeding":"econ.EM","tasks":"[\"econ.EM\",\"stat.ML\"]","methods":"[]","has_code":false}