Theory for high-order bounds in functional principal components analysis

By Peter Hall, Mohammad Hosseini-Nasab. Mathematical Proceedings of the Cambridge Philosophical Society, 2009

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Functional time series approach for forecasting very short-term electricity demand (2013, methodology): “Significant treatments of the theory of FPCA are given by Dauxois et al. [10], Cai and Hall [5], Hall et al. [17], Hall and Horowitz [15], and Hall and Hosseini-Nasab [16].”
Defining probability density for a distribution of random functions (2010, background): “Theoretical properties of empirical principal components are discussed by, for example, Hall and Hosseini-Nasab (2006, 2009).”
Truncated linear models for functional data (2014, unknown): “(See Hall and Hosseini-Nasab (2009).)”
A survey of functional principal component analysis (2014, methodology): “2005b), the analysis of spectroscopy data (Yao & Müller 2010), signal discrimination (Hall et al. 2001), and time-course gene expression (Yao et al. 2005a). Furthermore, Hyndman & Ullah (2007) proposed a smoothed and robust FPCA, and used it to forecast age-specific mortality and fertility rates.”
Nonasymptotic upper bounds for the reconstruction error of PCA (2016, background): “[11, 25, 14], spiked covariance models are often studied in the context of high-dimensional data [15, 8, 34].”
Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series (2013, background): “Silverman [36]), higher order theory (Hall and Hosseini-Nasab [18, 19]), nonparametric and conditional components (e.”