Some recent results in functional data analysis

BOENTE, GRACIELA

Londres

Workshop; Fourth Workshop of the ERCIM Working Group on Computing & Statistics; 2011

Functional data analysis provides modern analytical tools for data that are recoded as images or as a continuous phenomenon over a period of time. Because of the intrinsic nature of these data, they can be viewed as realizations of random functions often assumed to be in L2(I), with I a real interval or a finite dimensional Euclidean set. When working with more than one population, as in the finite dimensional case, a common assumption is to assume the equality of covariance operators. As in the multivariate setting, assuming equality of covariance operators is not satisfactory since the covariance operators may exhibit some common structure. We will briefly discuss the extension to the functional setting of the common principal component model that has been widely studied when dealing with multivariate observations. We present estimators of the unknown parameters as well as a robust approach for the common directions and their size related to the proposal given in the finite–dimensional setting. If possible, we will present a proposal for testing the hypothesis that the covariance operators of k populations of random objects are equal based on the norm of the difference among estimates of the operators.