Computational considerations in functional principal component analysis
Identificadores
URI: http://hdl.handle.net/10481/72993Metadatos
Mostrar el registro completo del ítemEditorial
Springer
Materia
Functional data analysis Hilbert spaces Principal components Covariance estimation Orthogonal projection
Fecha
2007-03-20Referencia bibliográfica
Ocaña, F.A., Aguilera, A.M. & Escabias, M. Computational considerations in functional principal component analysis. Computational Statistics 22, 449–465 (2007). https://doi.org/10.1007/s00180-007-0051-2
Patrocinador
Project MTM2004-5992 from Dirección General de Investigación, Ministerio de Ciencia y TecnologíaResumen
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.