Let X be a Gaussian rv with values in a separable Hilbert space H having a covariance operator R of the form R = L0*A*AL0, where L0, A are linear operators on H. A method is given for computing in terms of R0 = L0*L0 and A the distribution of X2, · being the norm in H. The result is applied...

[9] established multidimensional functional limit theorems for generalized U-statistics for estimable parameters which are stationary of order zero (the nondegenerate case). Similar univariate and bivariate functional limit theorems are derived for U-statistics in the degenerate case. The latter...

In this paper, we suggest the conditional test procedures for testing elliptical symmetry of multivariate distribution. The conditional tests are exactly valid if the symmetric center and the shape matrix are given and are asymptotically valid if they are unknowns to be estimated. The...

The paper presents some permutation test procedures for multivariate location. The tests are based on projected univariate versions of multivariate data. For one-sample cases, the tests are affine invariant and strictly distribution-free for the symmetric null distribution with elliptical...

The paper presents a permutation procedure for testing reflected (or diagonal) symmetry of the distribution of a multivariate variable. The test statistics are based in empirical characteristic functions. The resulting permutation tests are strictly distribution free under the null hypothesis...

The asymptotic power of the Cramér-von Mises test (CvM test) when parameters are estimated from the data is studied under certain local (contiguous) alternatives. The notion of (asymptotic) direction and distance from the null hypothesis of alternatives is introduced, and it is shown that there...