Functional regression modelling has become one of the most vibrant areas of research in the last years. This discussion provides some alternative approaches to one of the key issues of functional data analysis: the basis representation of curves, and in particular, of functional random effects. First, we propose the estimation of functional principal components by penalizing the norm, and as an alternative, we provide an efficient and unified approach based on B-spline basis and quadratic penalties.
AguileraAMAguilera-MorilloMC (2013) Penalized PCA approaches for B-spline expansions of smooth functional data. Applied Mathematics and Computation, 219, 7805–19.
2.
Aguilera-MorilloMDutranMAguileraAM (2016) Prediction of functional data with spatial dependence: A penalized approach. Stochastic Environmental Research and Risk Assessment, doi:10.1007/s00477-016- 1216-8.
3.
BrumbackBRiceJ (1998) Smoothing spline models for the analysis of nested and crossed samples of curves. Journal of the American Statistical Association, 93, 961–94.
4.
CurrieIDurbanMEilersP (2006) Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68, 259–80.
5.
DjeundjeVCurrieI (2010) Appropriate covariance-specification via penalties for penalized splines in mixed models for longitudinal data. Electronic Journal of Statistics, 2, 1202–24.
6.
DurbanMHarezlakJWandMCarrollR (2005) Simple fitting of subject-specific curves for longitudinal data. Statistics in Medicine, 24, 1153–67.
7.
EilersPHCMarxBD (1996) Flexible smoothing with B-splines and penalties. Statistical Science, 11, 107–21.
8.
MarraGWoodS (2012) Coverage properties of confidence intervals for generalized additive model components. Scandinavian Journal of Statistics, 39, 53–74.
9.
ReissPTOgdenRT (2007) Functional principal component regression and functional partial least squares. Journal of the American Statistical Association, 102, 984–96.
10.
Rodriguez-AlvarezMXDurbanMLeeD-J-JEilersPHC (2016) Fast estimation of multidimensional adaptive p-spline models. Technical report. Available at https://arxiv.org/abs/1610.06861
11.
Rodriguez-AlvarezMLeeD-JKneibTDurbanMEilersPHC (2015) Fast algorithm for smoothing parameter selection in multidimensional generalized p-splines. Statistics and Computing, 25, 241–57.
12.
ScheiplFGrevenS (2016) Identifiability in penalized function-on-function regression models. Electronic Journal of Statistics, 10, 495–526.
13.
SilvermanBW (1996) Smoothed functional principal component analysis by choice of norm. Annal Statistics, 24, 1–24.