On properties of functional principal components analysis

By Peter Hall, Mohammad Hosseini-Nasab. 2006

456 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0e44e537a1827f042795e22e21e962d0671b2b37

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Citations in the corpus

Peter Hall, functional data analysis and random objects (2016, background): “These developments were instrumental for a follow-up paper (Hall, Müller and Wang, 2006), where the results of Hall and Hosseini-Nasab (2006) and Yao, Müller and Wang (2005) were extended to systematically compare the estimation of eigenvalues and eigenfunctions for two sampling scenarios: A…”
Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics (2009, background): “(1996), Hall and Hosseini-Nasab (2006) and Hall et al. (2006), while Ramsay and Silver-”
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…”
Common functional principal components (2009, unknown): “The problem of determining a sensible upper limit of the number r0 of principal components to be analyzed is addressed in Hall and Hosseini-Nasab (2006).”
MULTILEVEL FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS (2009, background): “Wang (2005), while important theoretical results can be found in Hall and Hosseini-Nasab (2006).”
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.”
Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains (2015, background): “(A1) is a standard assumption in univariate FPCA (Bosq, 2000; Hall and Hosseini-Nasab, 2006).”
Dispersion operators and resistant second-order functional data analysis (2012, methodology): “…operator, and employing its spectral decomposition in order to probe the smoothness properties of the functional data; see Bosq (2000), Dauxois et al. (1982), Hall & Hosseini-Nasab (2006), Ramsay & Silverman (2005), Gervini (2006), Hall et al. (2006) and Yao & Lee (2006), to name but a few.”
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).”
Minimax adaptive tests for the Functional Linear model (2012, unknown): “[16], the convergence of the random eigenelements (λ̂j , V̂j) has been assessed from an asymptotic point of view [23, 24, 25, 31].”
Testing for lack of dependence in the functional linear model (2008, background): “This point is often overlooked in empirical work, but assumptions of this type are needed toevelop a rigorous asymptotic theory, see Bosq (2000, ch. 4) and Hall & Hosseini-Nasab (2006).”
Truncated linear models for functional data (2014, methodology): “…by using a standard method, and then estimating θ. Approaches that can be used to compute ǎ and b̌ are discussed by, for example, Ramsay and Silverman (2005), chapter 12, Hall and Hosseini-Nasab (2006) and Crambes et al. (2008, 2009); see Section 1 for a more detailed account of the literature.”
Presmoothing in Functional Linear Regression (2012, methodology): “In fact, Theorem 5 in Hall and Hosseini-Nasab (2006) gives conditions in order to find that E(‖θ − θ̂kn‖2) ∼ σ2 n kn∑ j=1 1 λ j + ‖Rkn‖2, where Rkn = ∑ j>kn 〈θ, vj〉vj , and Wn ∼ Zn means that the ratio of Wn and Zn converges to 1 when n → +∞.”
Componentwise classification and clustering of functional data (2012, methodology): “…p- dimensional projection ( ∫ I Xiϕ̂1, . . . , ∫ I Xiϕ̂p) T, where ϕ̂1, . . . , ϕ̂p were the first p eigenfunctions obtained by empirical principal component analysis (Hall and Hosseini-Nassab, 2006), and where p was chosen to minimize the cross-validation estimator of classification error defined…”