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

For high-dimensional small sample size data, Hotelling's T2 test is notapplicable for testing mean vectors due to the singularity problem in thesample covariance matrix. To overcome the problem, there are three mainapproaches in the literature. Note, however, that each of the existingapproaches may have serious limitations and only works well in certainsituations. Inspired by this, we propose a pairwise Hotelling method fortesting high-dimensional mean vectors, which, in essence, provides a goodbalance between the existing approaches. To effectively utilize the correlationinformation, we construct the new test statistics as the summation ofHotelling's test statistics for the covariate pairs with strong correlationsand the squared $t$ statistics for the individual covariates that have littlecorrelation with others. We further derive the asymptotic null distributionsand power functions for the proposed Hotelling tests under some regularityconditions. Numerical results show that our new tests are able to control thetype I error rates, and can achieve a higher statistical power compared toexisting methods, especially when the covariates are highly correlated. Tworeal data examples are also analyzed and they both demonstrate the efficacy ofour pairwise Hotelling tests.

A Pairwise Hotelling Method for Testing High-Dimensional Mean Vectors