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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

In this work we construct an optimal linear shrinkage estimator for thecovariance matrix in high dimensions. The recent results from the random matrixtheory allow us to find the asymptotic deterministic equivalents of the optimalshrinkage intensities and estimate them consistently. The developeddistribution-free estimators obey almost surely the smallest Frobenius lossover all linear shrinkage estimators for the covariance matrix. The case weconsider includes the number of variables $p\rightarrow\infty$ and the samplesize $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$.Additionally, we prove that the Frobenius norm of the sample covariance matrixtends almost surely to a deterministic quantity which can be consistentlyestimated.

On the Strong Convergence of the Optimal Linear Shrinkage Estimator for Large Dimensional Covariance Matrix