No abstract

We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika 65, 657-658) of the d-dimensional data on the unit sphere of R d . We find, under mild hypothesis, the limiting null distribution of the statistic presented, showing that, for an appropriate choice of the spherical harmonics included in the statistic, this distribution does not depend on the parameters that characterize the underlying elliptically symmetric law. We describe a bivariate simulation study that shows that the finite sample quantiles of our statistic converge fairly rapidly, with sample size, to the theoretical limiting quantiles and that our procedure enjoys good power against several alternatives.

Binary splitting, Blck clustering, Markov chain simulation method, Permutation distribution,

No abstract

Empirical processes, hypothesis testing, multivariate normality, spherical harmonics, primary: 62F03, 62E20, secondary: 60F17,