Testing the Equality of Covariance Operators in Functional Samples

We propose a robust 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 performance is examined by a simulation study and an application to egg-laying curves of fruit flies.