Functional canonical analysis for square integrable stochastic processes

By G. He, H. Muller, Jane-ling Wang. 2003

127 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/729258ca54d372b1025e11272718da9c1bd60b50

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Citations in the corpus

CLT in functional linear regression models (2005, methodology): “…regression can be viewed as an ill-conditioned inverse problem since the estimation procedure relies on the inversion of the covariance operator which is compact (Cardot et al. 1999, Bosq 2000, He et al. 2003) and it is well known that poor rates of convergence appear for this kind of problems.”
Canonical correlation for stochastic processes (2008, background): “He, Müller and Wang [13] (denoted by HMW herafter) developed a notion of canonical correlation for processes of the form (34) through a direct extension of finite-dimensional matrix formulations with integral operators being used in the place of matrices.”
On properties of functional principal components analysis (2006, background): “…(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. (1999)) and applications of PCA to fields as diverse as longitudinal data…”
Functional Modelling and Classification of Longitudinal Data. (2005, methodology): “This involves the inversion of a compact operator (He et al., 2003) and therefore requires sensible regularization, as proposed in Leurgans et al.”
Functional Data Analysis (2016, methodology): “…inverse to the range A X of Σ 1 / 2 XX so that the inverse of Σ 1 / 2 XX can be deﬁned on A X and is a bijective mapping A X to B X , under some conditions (e.g., Conditions 4.1 and 4.5 in He, M¨uller & Wang (2003)) on the decay rates of the eigenvalues of Σ XX and Σ Y Y and the cross-covariance.”
FUNCTIONAL RESPONSE MODELS (2004, methodology): “Such models have been investigated recently by Cardot, Ferraty and Sarda (1999), Cardot, Ferraty, Mas and Sarda (2003), James (2002), Ratcliffe, Heller and Leader (2002) and Müller and Stadtmüller (2004).”
Functional Additive Models (2008, unknown): “By solving a “functional population normal equation” (He, Müller, and Wang 2000, 2003), we obtain for scalar (resp. functional) responses β(s) = ∞∑ k=1 E(ξkY ) E(ξ2k ) φk(s) and (3) β(s, t) = ∞∑ k=1 ∞∑ m=1 E(ξkζm) E(ξ2k ) φk(s)ψm(t).”
Functional singular component analysis (2011, background): “We demonstrate the estimation of the resulting singular values, functions and components for the practically relevant case of sparse and noise-contaminated longitudinal data and provide asymptotic consistency results.”
Curve Forecasting by Functional Autoregression (2008, background): “…since 1112 Γ=Γ ρ , operator Φ has an alternative representation, 2/1 111221 2/1 11 −− ΓΓΓΓ=Φ , reminiscent of the cross-correlation operator 2/12/1 −− ΓΓΓ YYXYXX playing the key role in He et al. (2003) study of the existence of functional canonical correlations for functional processes X and Y .”
Dynamical Correlation for Multivariate Longitudinal Data (2005, methodology): “This latter method is discussed and evaluated under the rubric ”smoothing and subsequent subsampling” (Method 1, FCA-LP) in He et al., (2004), where various implementations of functional canonical correlation are compared.”
Assessing the finite dimensionality of functional data (2006, background): “…field is very extensive; it extends well into related areas, such as longitudinal data analysis, and is discussed in these books and in papers by Capra and Müller (1997), Brumback and Rice (1998), Staniswalis and Lee (1998), Cardot et al. (1999, 2003) and He et al. (2003), to list only a very few.”
Functional linear regression via canonical analysis (2010, background): “Leurgans, Moyeed and Silverman (1993) tackled the difficult problem of extending CCA to the case of infinite-dimensional functional data and discussed the precarious regularization issues which are faced; He, Müller and Wang (2003, 2004) further explored various aspects and proposed practically feas”