Testing the equality of covariance operators in functional samples

ABSTRACT. We propose a robust test for the equality of the covariance struc-tures in two functional samples. The test statistic has a chi-square asymptotic dis-tribution 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 asymp-totic properties is developed. Finite sample performance is examined by a simulation study and an application to egg–laying curves of fruit flies