The general machinery of Cordeiro and Ferrari (1991. Biometrika 78. 573-582
) and Chandra and Mukerjee (1991. J. Multivariate Anal. 36. 103-112) provid
es modifications of score rest statistics which bring the null distribution
s close to their large-sample asymptotic distributions. These modifications
are calculated here For the Rayleigh and Bingham tests of uniformity on sp
heres of arbitrary dimension. Stiefel manifolds, rotation groups. Grassmann
manifolds and complex projective spaces. (C) 2001 Academic Press.