This paper is motivated by the problem of detecting local changes
or differences in shape between two samples of objects via the nonlinear
deformations required to map each object to an atlas standard. Local shape
changes are then detected by high values of the random field of
Hotelling’s $T^2$ statistics for detecting a change in mean of the
vector deformations at each point in the object. To control the null
probability of detecting a local shape change, we use the recent result of
Adler that the probability that a random field crosses a high threshold is very
accurately approximated by the expected Euler characteristic (EC) of the
excursion set of the random field above the threshold. We give an exact
expression for the expected EC of a Hotelling’s $T^2$ field, and we
study the behavior of the field near local extrema. This extends previous
results for Gaussian random fields by Adler and $\chi^2$, $t$ and $F$ fields by
Worsley and Cao. For illustration, these results are applied to the detection
of differences in brain shape between a sample of 29 males and 23 females.
Publié le : 1999-06-14
Classification:
Local extrema,
Euler characteristic,
excursion set,
random fields,
Hotelling's $T^2$,
brain mapping,
60G60,
62M09,
60D05,
52A22
@article{1018031263,
author = {Cao, Jin and Worsley, Keith J.},
title = {The detection of local shape changes via the geometry of
Hotelling's $T^2$ fields},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 925-942},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031263}
}
Cao, Jin; Worsley, Keith J. The detection of local shape changes via the geometry of
Hotelling's $T^2$ fields. Ann. Statist., Tome 27 (1999) no. 4, pp. 925-942. http://gdmltest.u-ga.fr/item/1018031263/