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

Let $S_{p,n}$ denote the sample covariance matrix based on $n$ independentidentically distributed $p$-dimensional random vectors in the null-case. Themain result of this paper is an explicit expansion of trace moments andpower-trace covariances of $S_{p,n}$ simultaneously for both high- andlow-dimensional data. To this end we expand a well-known ansatz of describingtrace moments as weighted sums over routes or graphs. The novelty to ourapproach is an inherent coloring of the examined graphs and a decomposition ofgraphs into their tree-structure and their \textit{seed graphs}, which allowsfor some elegant formulas explaining the effect of the tree structures on thenumber of Euler-tours. The weighted sums over graphs become weighted sums overthe possible seed graphs, which in turn are much easier to analyze.

Trace Moments of the Sample Covariance Matrix with Graph-Coloring