Abstract
The statistical problem addressed in this paper to approximate the P-value of the maximum of a smooth random field of Wilks's Lambda statistics. So far results are only available for the usual univariate statistics (Z, t, chi2, F) and a few multivariate statistics (Hotelling's T2, maximum canonical correlation, Roy's maximum root). We derive results for any differentiable scalar function of two independent Wishart random fields, such as Wilks's Lambda and Pillai's trace. We apply our results to a problem in brain shape analysis.