@misc{10481/72993,
year = {2007},
month = {3},
url = {http://hdl.handle.net/10481/72993},
abstract = {Computing estimates in functional principal component analysis
(FPCA) from discrete data is usually based on the approximation of sample
curves in terms of a basis (splines, wavelets, trigonometric functions, etc.) and
a geometrical structure in the data space (L2 spaces, Sobolev spaces, etc.).
Until now, the computational efforts have been focused in developing ad hoc
algorithms to approximate those estimates by previously selecting an efficient
approximating technique and a convenient geometrical structure. The main
goal of this paper consists of establishing a procedure to formulate the algorithm for computing estimates of FPCA under general settings. The resulting
algorithm is based on the classic multivariate PCA of a certain random vector
and can thus be implemented in the majority of statistical packages. In fact, it
is derived from the analysis of the effects of modifying the norm in the space of
coordinates. Finally, an application on real data will be developed to illustrate
the so derived theoretic results.},
organization = {Project MTM2004-5992 from Dirección General de Investigación, Ministerio de Ciencia y Tecnología},
publisher = {Springer},
keywords = {Functional data analysis},
keywords = {Hilbert spaces},
keywords = {Principal components},
keywords = {Covariance estimation},
keywords = {Orthogonal projection},
title = {Computational considerations in functional principal component analysis},
doi = {https://doi.org/10.1007/s00180-007-0051-2},
author = {Ocaña Lara, Francisco Antonio and Aguilera Del Pino, Ana María and Escabias Machuca, Manuel},
}