Optimal Estimation for a Class of High‐Dimensional Covariance Matrices
Huimin Li & Youming Liu
What the paper says
Estimation of large covariance matrices plays important roles in high‐dimensional data analysis. The sub‐Gaussian condition of a random vector is usually assumed, which requires the existence of infinite moments. Avella‐Medina et al. (2018) provide an upper bound estimation in the sense of probability over a sparse covariance matrix space under the weak assumption of bounded moments (), see Biometrika, 105, 271–284. In particular, their estimation attains the minimax optimality when . The authors conjecture that their estimation is optimal as well for . In this paper, we first extend their upper bound estimation to a larger space and then prove the optimality of our estimation. This can be considered as a solution to their conjecture. Moreover, we give an optimal estimation in terms of expectation on the same space. Finally, numerical experiments support our theoretical analysis.
Evidence weight
Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40
| F · citation impact | 0.50 × 0.4 = 0.20 |
| M · momentum | 0.50 × 0.15 = 0.07 |
| V · venue signal | 0.50 × 0.05 = 0.03 |
| R · text relevance † | 0.50 × 0.4 = 0.20 |
† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.