Nonparametric estimation of smoothed principal components analysis of sampled noisy functions

By Hervé Cardot. 2000

98 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/56ded2af0ed4ff1789365db79d799f1020461562

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Citations in the corpus

Functional Data Analysis (2016, background): “…Pousse & Romain (1982), Besse & Ramsay (1986); Silverman (1996), Bosq (2000); Boente & Fraiman (2000); Hall & Hosseini-Nasab (2006), and it was explored for densely observed functional data in Castro, Lawton & Sylvestre (1986); Rice & Silverman (1991); Pezzulli & Silverman (1993) and Cardot (2000).”
Properties of design-based functional principal components analysis (2008, background): “More recent works deal with smoothing or interpolation procedures (Castro et al., 1986, Besse and Ramsay, 1986, Cardot, 2000 or Benko et al. 2009) as well as bootstrap properties (Kneip and Utikal, 2001) or sparse data (James et al., 2000).”
Prediction in functional linear regression (2006, result): “There are a great many more recent contributions, including those of Brumback and Rice [5], Cardot [7], Cardot, Ferraty and Sarda [8–10], Girard [19], James, Hastie and Sugar [23], Boente and Fraiman [3] and He, Müller and Wang [21].”
Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series (2013, background): “Cardot [10, 11]) and components for irregularly sampled functional data (e.”
COVARIATE ADJUSTED FUNCTIONAL PRINCIPAL COMPONENTS ANALYSIS FOR LONGITUDINAL DATA (2010, methodology): “This is different from the situation considered in Cardot (2006) where a covariate adjusted FPCA was proposed under the assumption that the entire function X(t, z) can be observed without errors.”
Functional Modelling and Classification of Longitudinal Data. (2005, background): “The importance of smoothing in the estimation of functional principal components has been emphasized in Rice & Silverman (1991), Capra & Muïler (1997), Boente & Fraiman (2000) and Cardot (2000).”
Functional Modelling and Classification of Longitudinal Data * (2005, background): “The importance of smoothing in the estimation of functional principal components has been emphasized in Rice & Silverman (1991), Capra & Müller (1997), Boente & Fraiman (2000) and Cardot (2000).”
A Geometric Approach to Maximum Likelihood Estimation of the Functional Principal Components From Sparse Longitudinal Data (2007, methodology): “For example, Cardot (2006) studied a model where the covariance of X(·) conditioned on a covariate W has the expansion C(s, t) := cov(X(s),X(t)|W = w) = ∑ ν≥1 λν(w)ψν(s,w)ψν(t,w).”
On properties of functional principal components analysis (2006, methodology): “More recent research includes contributions to techniques for functional PCA (see for example Brumback and Rice (1998), Cardot (2000), Cardot et al. (2000), Girard (2000), James et al. (2000), Boente and Fraiman (2000) and He et al. (2003)), functional PCA in different metrics (e.g. Ocana et al.…”
Smoothing splines estimators for functional linear regression (2009, background): “The distance between α̂ and α is evaluated with respect to L2 semi-norms induced by the operator Γ, ‖u‖2Γ = 〈Γu,u〉 with 〈u, v〉 = ∫I u(t)v(t)dt, or its discretized or empirical versions (see, e.g., Cardot, Ferraty and Sarda [7] or Müller and Stadtmüller [23] for similar setups).”