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 consider an inference on the eigenvalues of the covariance matrix of amultivariate normal distribution. The family of multivariate normaldistributions with a fixed mean is seen as a Riemannian manifold with Fisherinformation metric. Two submanifolds naturally arises; one is the submanifoldgiven by fixed eigenvectors of the covariance matrix, the other is the onegiven by fixed eigenvalues. We analyze the geometrical structures of thesemanifolds such as metric, embedding curvature under $e$-connection or$m$-connection. Based on these results, we study 1) the bias of the sampleeigenvalues, 2)the information loss caused by neglecting the sampleeigenvectors, 3)new estimators that are naturally derived from the geometricalview.

Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution--geometrical view--