We congratulate the authors for their excellent work that provides a clear overview of the large and now mature field of regression models for functional data. We here complement their discussion indicating some directions of further research that we deem particularly important.
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ChenDMüllerH-G (2012) Nonlinear manifold representations for functional data. The Annals of Statistics, 40, 1–29.
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ClaeskensG, HubertM, SlaetsLVakiliK (2014) Multivariate functional halfspace depth. Journal of the American Statistical Association, 109, 411–23.
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GhigliettiA, IevaF, PaganoniAAlettiG (2015) On linear regression models in infinite dimensional spaces with scalar response. In press, DOI 10.1007/s00362-015-0710-2.
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HadjipantelisPZ, AstonJAD, MüllerH-GMoriartyJ (2014) Analysis of spike train data: A multivariate mixed effects model for phase and amplitude [mr3273592]. Electronic Journal of Statistics, 8, 1797–1807.
10.
HadjipantelisPZ, AstonJAD, MüllerH-GEvansJP (2015) Unifying amplitude and phase analysis: A compositional data approach to functional multivariate mixed-effects modeling of Mandarin Chinese. Journal of the American Statistical Association, 110, 545–59.
11.
HorváthLKokoszkaP (2012) Inference for functional data with applications. New York, NY: Springer.
12.
HronK, MenafoglioA, TemplM, HruzováKFilzmoserP (2016) Simplicial principal component analysis for density functions in Bayes spaces. Computational Statistics & Data Analysis, 94, 330–50.
13.
IevaFPaganoniA (2013) Depth measures for multivariate functional data. Communication in Statistics—Theory and Methods, 42, 1265–76.
14.
IgnaccoloR, MateuJGiraldoR (2014) Kriging with external drift for functional data for air quality monitoring. Stochastic Environmental Research and Risk Assessment, 28, 1171–86.
15.
KneipARamsayJO (2008) Combining reg- istration and fitting for functional models. Journal of the American Statistical Association, 103, 1155–65.
Lopez-PintadoSRomoJ (2007) Depth-based inference for functional data. Computatio- nal Statistics & Data Analysis, 51, 4957–68.
18.
Lopez-PintadoSRomoJ (2009) On the concept of depth for functional data. Journal of the American Statistical Association, 104, 718–34.
19.
Lopez-PintadoS, SunYGentonM (2014) Simplicial band depth for multivariate functional data. Advances in Data Analysis and Classification, 8, 321–38.
20.
MarronJS, RamsayJO, SangalliLM, SrivastavaA (2014) Statistics of time warpings and phase variations. Electronic Journal of Statistics, 8, 1697–1702.
21.
MarronJS, RamsayJO, SangalliLM, SrivastavaA (2015) Functional data analysis of amplitude and phase variation. Statistical Science, 30, 468–84.
22.
MenafoglioA, SecchiPDalla RosaM (2013) A universal kriging predictor for spatially dependent functional data of a Hilbert Space. Electronic Journal of Statistics, 7, 2209–40.
23.
MenafoglioA, GuadagniniASecchiP (2014) A kriging approach based on Aitchison geometry for the characterization of particle-size curves in heterogeneous aquifers. Stochastic Environmental Research and Risk Assessment, 28, 1835–51.
24.
PiniAVantiniS (2016) The interval testing procedure: A general framework for inference in functional data analysis. Biometrics, 72, 835–45.
25.
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26.
SangalliLM, SecchiP, VantiniSVitelliV (2010) K-mean alignment for curve clustering. Computational Statistics & Data Analysis, 54, 1219–33.
27.
SangalliLM, RamsayJORamsayTO (2013) Spatial spline regression models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75, 681–703.
28.
SangalliLM, SecchiPVantiniS (2014) Analysis of AneuRisk65 data: K-mean alignment. Electronic Journal of Statistics, 8, 1891–1904.
29.
TarabelloniN, IevaF, BiasiRPaganoniA (2015) Use of depth measure for multivariate functional data in disease prediction: An application to electrocardiographic signals. The International Journal of Biostatistics, 11, 189–201.
