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

A common feature of high-dimensional data is that the data dimension is high,however, the sample size is relatively low. We call such data HDLSS data. Inthis paper, we study asymptotic properties of the first principal component inthe HDLSS context and apply them to equality tests of covariance matrices forhigh dimensional data sets. We consider HDLSS asymptotic theories as thedimension grows for both the cases when the sample size is fixed and the samplesize goes to infinity. We introduce an eigenvalue estimator by thenoise-reduction methodology and provide asymptotic distributions of the largesteigenvalue in the HDLSS context. We construct a confidence interval of thefirst contribution ratio. We give asymptotic properties both for the first PCdirection and PC score as well. We apply the findings to equality tests of twocovariance matrices in the HDLSS context. We provide numerical results anddiscussions about the performances both on the estimates of the first PC andthe equality tests of two covariance matrices.

Asymptotic properties of the first principal component and equality tests of covariance matrices in high-dimension, low-sample-size context