Testing the Equality of Covariance Operators in Functional Samples


Josef G. Steinebach, Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Köln, Germany.
E-mail: jost@math.uni-koeln.de


Abstract.  We propose a non-parametric test for the equality of the covariance structures in two functional samples. The test statistic has a chi-square asymptotic distribution with a known number of degrees of freedom, which depends on the level of dimension reduction needed to represent the data. Detailed analysis of the asymptotic properties is developed. Finite sample perfo-rmance is examined by a simulation study and an application to egg-laying curves of fruit flies.