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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We develop a method for estimating well-conditioned and sparse covariance andinverse covariance matrices from a sample of vectors drawn from a sub-gaussiandistribution in high dimensional setting. The proposed estimators are obtainedby minimizing the quadratic loss function and joint penalty of `1 norm andvariance of its eigenvalues. In contrast to some of the existing methods ofcovariance and inverse covariance matrix estimation, where often the interestis to estimate a sparse matrix, the proposed method is flexible in estimatingboth a sparse and well-conditioned covariance matrix simultaneously. Theproposed estimators are optimal in the sense that they achieve the minimax rateof estimation in operator norm for the underlying class of covariance andinverse covariance matrices. We give a very fast algorithm for computation ofthese covariance and inverse covariance matrices which is easily scalable tolarge scale data analysis problems. The simulation study for varying samplesizes and variables shows that the proposed estimators performs better thanseveral other estimators for various choices of structured covariance andinverse covariance matrices. We also use our proposed estimator for tumortissues classification using gene expression data and compare its performancewith some other classification methods.

A Well-Conditioned and Sparse Estimation of Covariance and Inverse Covariance Matrices Using a Joint Penalty