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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Our data are random fields of multivariate Gaussian observations, and we fita multivariate linear model with common design matrix at each point. We areinterested in detecting those points where some of the coefficients are nonzerousing classical multivariate statistics evaluated at each point. The problem isto find the $P$-value of the maximum of such a random field of test statistics.We approximate this by the expected Euler characteristic of the excursion set.Our main result is a very simple method for calculating this, which not onlygives us the previous result of Cao and Worsley [Ann. Statist. 27 (1999)925--942] for Hotelling's $T^2$, but also random fields of Roy's maximum root,maximum canonical correlations [Ann. Appl. Probab. 9 (1999) 1021--1057],multilinear forms [Ann. Statist. 29 (2001) 328--371], $\bar{\chi}^2$ [Statist.Probab. Lett 32 (1997) 367--376, Ann. Statist. 25 (1997) 2368--2387] and$\chi^2$ scale space [Adv. in Appl. Probab. 33 (2001) 773--793]. The trickinvolves approaching the problem from the point of view of Roy'sunion-intersection principle. The results are applied to a problem in shapeanalysis where we look for brain damage due to nonmissile trauma.

Random fields of multivariate test statistics, with applications to shape analysis