Comparative study of different B-spline approaches for functional data
MetadataShow full item record
Functional dataB-spline expansionsRoughness penaltyP-splines
A.M. Aguilera, M.C. Aguilera-Morillo, Comparative study of different B-spline approaches for functional data, Mathematical and Computer Modelling, Volume 58, Issues 7–8, 2013, Pages 1568-1579, ISSN 0895-7177, https://doi.org/10.1016/j.mcm.2013.04.007
SponsorshipProject MTM2010-20502 from Dirección General de Investigación, Ministerio de Educación y Ciencia Spain; Project P11-FQM-8068 from Consejería de Innovación, Ciencia y Empresa. Junta de Andalucía, Spain
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.