Testing equality between several populations covariance operators

BOENTE, G.; RODRIGUEZ, D.; SUED, M.

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS

SPRINGER HEIDELBERG

Lugar: HEIDELBERG; Año: 2017

0020-3157

In many situations, when dealing with several populations, equality of the covariance  operators is assumed. An important issue is tostudy whether this assumption holds before making other inferences. In this paper, we develop a test for comparing covariance operators ofseveral functional data samples. The proposed test is based on the Hilbert--Schmidt norm of  the difference between   estimated covariance operators. In particular, when dealing with two populations, the test statistic is just the squared norm of the  difference between the two   covariance operators estimators. The  asymptotic behaviour of the test statistic under both the null hypothesis and   local  alternatives  is obtained.  The computation of the quantiles of the null asymptotic  distribution  is not feasible in practice. To overcome this problem,  a   bootstrap procedure is considered. The performance of the test statistic  for small sample sizes is illustrated through a Monte Carlo study and on a real data set.