Abstract.
Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively used in practical situations. In this work we focus on local covariance operators. They provide some pieces of information about the distribution of X around a fixed point of the space x 0. A description of the asymptotic behaviour of the theoretical and empirical counterparts is carried out. Asymptotic developments are given under assumptions on the location of x 0 and on the distributions of projections of the data on the eigenspaces of the (non-local) covariance operator.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Daniel Alpay.
Received: March 5, 2007. Accepted: July 6, 2007.
Rights and permissions
About this article
Cite this article
Mas, A. Local Functional Principal Component Analysis. Complex anal.oper. theory 2, 135–167 (2008). https://doi.org/10.1007/s11785-007-0026-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11785-007-0026-x