Functional principal component analysis (FPCA) based on the Karhunen-Loève decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not...

We present two methods based on functional principal component analysis (FPCA) for the estimation of smooth derivatives of a sample of random functions, which are observed in a more than one-dimensional domain.We apply eigenvalue decomposition to a) the dual covariance matrix of the derivatives,...