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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2507.04663 |
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| _version_ | 1866915652515659776 |
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| author | Stojnic, Mehmet Caner Agostino Capponi Mihailo |
| author_facet | Stojnic, Mehmet Caner Agostino Capponi Mihailo |
| contents | 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\&P 500 index, where we observe a doubly ascending Sharpe ratio pattern, which complements the double descent phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Model-Estimation-Free, Dense, and High Dimensional Consistent Precision Matrix Estimators Stojnic, Mehmet Caner Agostino Capponi Mihailo Econometrics Machine Learning 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\&P 500 index, where we observe a doubly ascending Sharpe ratio pattern, which complements the double descent phenomenon. |
| title | Model-Estimation-Free, Dense, and High Dimensional Consistent Precision Matrix Estimators |
| topic | Econometrics Machine Learning |
| url | https://arxiv.org/abs/2507.04663 |