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February 2008 Random fields of multivariate test statistics, with applications to shape analysis
J. E. Taylor, K. J. Worsley
Ann. Statist. 36(1): 1-27 (February 2008). DOI: 10.1214/009053607000000406

Abstract

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 T2, 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], χ̄2 [Statist. Probab. Lett 32 (1997) 367–376, Ann. Statist. 25 (1997) 2368–2387] and χ2 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.

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J. E. Taylor. K. J. Worsley. "Random fields of multivariate test statistics, with applications to shape analysis." Ann. Statist. 36 (1) 1 - 27, February 2008. https://doi.org/10.1214/009053607000000406

Information

Published: February 2008
First available in Project Euclid: 1 February 2008

zbMATH: 1144.62083
MathSciNet: MR2387962
Digital Object Identifier: 10.1214/009053607000000406

Subjects:
Primary: 52A22 , 62H11

Keywords: Canonical correlation , differential topology , Euler characteristic , Hotelling’s T^2 , integral geometry , Morse theory , Roy’s maximum root , scale space

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 1 • February 2008
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