Assessing the finite dimensionality of functional data

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Long-Range Dependent Curve Time Series (2020, methodology): “Other dimension selection methods proposed in the literature such as cross-validation (Hall and Hosseini-Nasab 2006), bootstrap (Hall and Vial 2006), minimum description length (Poskitt and Sengarapillai 2013), and Akaike information criterion (Li, Wang, and Carroll 2013) may also be applicable to e”
Defining probability density for a distribution of random functions (2010, background): “See, for example, Horn (1965), Velicer (1976), Zwick and Velicer (1986), Peres-Neto, Jackson and Somers (2005) and Hall and Vial (2006).”
A survey of functional principal component analysis (2014, methodology): “( 2005b ) , Hall & Horowitz ( 2007 ) , Hall & Hosseini - Nasab ( 2006 ) , Hall & Vial ( 2006 ) , Hall et al .”
Peter Hall, functional data analysis and random objects (2016, background): “This question was studied by Peter for the difficult situation where one has additional noise and discrete measurements of the functional data in Hall and Vial (2006a), where some asymptotically motivated criteria were proposed.”
Fourier analysis of stationary time series in function space (2013, methodology): “Under this weak assumption, we formalise the asymptotic discrete observation framework via observation on an increasingly dense grid subject to measurement error of variance decreasing at a certain rate [e.g., Hall and Vial (2006)].”