English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Consider n independent and identically distributed p-dimensional Gaussian random vectors with covariance matrix &#x03A3;. The problem of estimating &#x03A3; when p is much larger than n has received a lot of attention in recent years. Yet, little is known about the information criterion for covariance matrix estimation. How to properly define such a criterion and what are the statistical properties? We attempt to answer these questions in this paper by focusing on the estimation of bandable covariance matrices when p &gt; n but log(p) = o(n). Motivated by the deep connection between Stein's unbiased risk estimation (SURE) and Akaike information criterion (AIC) in regression models, we propose a family of generalized SURE (SUREc) indexed by c for covariance matrix estimation, where c is some constant. When c is 2, SURE2 provides an unbiased estimator of the Frobenius risk of the covariance matrix estimator. Furthermore, we show that by minimizing SURE2 over all possible banding covariance matrix estimators, we attain the minimax optimal rate of convergence under the Frobenius norm, and the resulting estimator behaves like the covariance matrix estimator obtained by the so-called oracle tuning. When the true covariance matrix is exactly banded, we prove that by minimizing SURE<sub>log(n)</sub>, we select the true bandwidth with probability tending to one. Therefore, our analysis indicates that SURE2 and SURE<sub>log(n)</sub> can be regarded as the AIC and Bayesian information criterion for large covariance matrix estimation, respectively.

SURE Information Criteria for Large Covariance Matrix Estimation and Their Asymptotic Properties