@misc{10481/72950,
year = {2013},
month = {4},
url = {http://hdl.handle.net/10481/72950},
abstract = {The sample observations of a functional variable are functions that come from the
observation of a statistical variable in a continuous argument that in most cases is the
time. But in practice, the sample functions are observed in a finite set of points. Then, the
first step in functional data analysis is to reconstruct the functional form of sample curves
from discrete observations. The sample curves are usually represented in terms of basis
functions and the basis coefficients are fitted by interpolation, when data are observed
without error, or by least squares approximation, in the other case. The main purpose of
this paper is to compare three different approaches for estimating smooth sample curves
observed with error in terms of B-spline basis: regression splines (non-penalized least
squares approximation), smoothing splines (continuous roughness penalty) and P-splines
(discrete roughness penalty). The performance of these spline smoothing approaches is
studied via a simulation study and several applications with real data. Cross-validation and
generalized cross-validation are adapted to select a common smoothing parameter for all
sample curves with the roughness penalty approaches. From the results, it is concluded
that both penalized approaches drastically reduced the mean squared errors with respect
to the original smooth sample curves with P-splines giving the best approximations with
less computational cost.},
organization = {Project MTM2010-20502 from Dirección General de Investigación, Ministerio de Educación y Ciencia Spain},
organization = {Project P11-FQM-8068 from Consejería de Innovación, Ciencia y Empresa. Junta de Andalucía, Spain},
publisher = {Elsevier},
keywords = {Functional data},
keywords = {B-spline expansions},
keywords = {Roughness penalty},
keywords = {P-splines},
title = {Comparative study of different B-spline approaches for functional data},
doi = {https://doi.org/10.1016/j.mcm.2013.04.007},
author = {Aguilera Del Pino, Ana María and Aguilera Morillo, María del Carmen},
}