Theoretical foundations of functional data analysis, with an introduction to linear operators

2015

790 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/433a087b070a4f1a0d68225a89d403b49ad7ac05

Citations in the corpus

• Prediction of functional ARMA processes with an application to traffic data (2016, methodology): “For details and more background we refer to the monographs Bosq [3], Horv`ath and Kokoszka [8] and Hsing and Eubank [9].”
• Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes (2019, methodology): “Let H(s, t) = ∑∞ l=1 τlηl(s)ηl(t), be the unique Mercer expansion [14], where ηl form an orthonormal sequence in L 2[0, 1] and τl is a nonincreasing sequence of positive numbers with ∑∞ l=1 τl <∞.”
• Distribution-on-Distribution Regression via Optimal Transport Maps (2021, background): “Functional data analysis [5] considers statistical inference problems whose sample and parameter spaces constitute function spaces.”
• Partially Linear Functional Additive Models for Multivariate Functional Data (2018, methodology): “Both assumptions are widely used in the FLM literature (Cai and Hall 2006; Cai and Yuan 2012; Hsing and Eubank 2015).”
• Fréchet means and Procrustes analysis in Wasserstein space (2017, background): “Hsing & Eubank [41]) and non-Euclidean statistics (e.”
• Nonlinear sufficient dimension reduction for functional data (2017, background): “For more information about Moore–Penrose inverse in this setting, see Hsing and Eubank (2015), Section 3.5.”
• Testing for stationarity of functional time series in the frequency domain (2017, background): “M E ] 8 O ct 2 may consult Bosq (2000), Ferraty & Vieu (2010), Horváth & Kokoszka (2012), Hsing & Eubank (2015) and Ramsay & Silverman (2005).”
• Principal component analysis for functional data on Riemannian manifolds and spheres (2017, methodology): “One obtains the Karhunen-Loève decomposition (see for example Hsing and Eubank 2015), V (t) = ∞∑ k=1 ξkφk(t), (5) where ξk = ∫ T V (t)φk(t)dt is the kth Riemannian functional principal component (RFPC) score, k = 1, 2, . . . .”
• High-dimensional geometry of population responses in visual cortex (2018, positive): “This approach, known as functional data analysis, has not yet been commonly applied in neuroscience, but has a well-developed theoretical basis thanks to applications in other domains [29, 4].”
• Functional Data Analysis (2016, methodology): “…smoothing methods, notably kernel, local least squares and spline smoothing for which various excellent reference books exist (Wand & Jones 1995; Fan & Gijbels 1996; Eubank 1999; de Boor 2001), functional analysis (Conway 1994; Hsing & Eubank 2015) and stochastic processes (Ash & Gardner 1975).”
• Nonasymptotic upper bounds for the reconstruction error of PCA (2016, background): “In [18, 13] the remainder term is given by an integral over the resolvent, while the above results lead to an algebraic form of the remainder term.”