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

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

2008-03-12

arxiv.org/abs/0803.1708v1

Annals of Statistics 2008, Vol. 36, No. 1, 1-27

Mathematics

Statistics Theory

Published in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.ims

Scientific paper

10.1214/009053607000000406

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to 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 only gives 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 trick involves approaching the problem from the point of view of Roy's union-intersection principle. The results are applied to a problem in shape analysis where we look for brain damage due to nonmissile trauma.

Affiliated with

Also associated with

No associations

Rating

Random fields of multivariate test statistics, with applications to shape analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random fields of multivariate test statistics, with applications to shape analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random fields of multivariate test statistics, with applications to shape analysis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-369359