Functional Principal Component Regression and Functional Partial Least Squares

By Philip T. Reiss, Todd Ogden. 2007

332 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Biophysics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b328a8ecb6261a56c7fe7ea3d2a57c0a9931d0a4

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Citations in the corpus

Smoothing parameter selection for a class of semiparametric linear models (2009, neutral): “In the functional regression literature, Marx and Eilers (1999) proposed ordinary cross-validation, whereas Cardot et al. (2003) used GCV; REML yielded superior results in the simulations of Reiss and Ogden (2007).”
Applications of functional data analysis: A systematic review (2013, background): “Application of FDA has also been published across various scientific fields including analysis of child size evolution [9], climatic variation [4,13], handwriting in Chinese [14], acidification processes [15], land usage prediction based on satellite images [16], medical research [17-19], behavioral”
A survey of functional principal component analysis (2014, methodology): “As a powerful dimension reduction tool ( as shown in Section 3 ) , FPCA has been extensively used to regularize ill - conditioned estimators in functional regression models ( see for example , Reiss & Ogden 2007 ) .”
Functional time series approach for forecasting very short-term electricity demand (2013, background): “[18], Reiss and Ogden [34], Shen [37], and Hyndman and Shang [23].”
Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models (2011, methodology): “For more detail on such models see Marx and Eilers (1999), Escabias et al. (2004), Ramsay and Silverman (2005) or Reiss and Ogden (2007) (and also Wahba (1990)).”
Rainbow Plots, Bagplots, and Boxplots for Functional Data (2010, background): “Such functional data may be age-speciﬁc mortality or fertility rates (Hyndman & Ullah 2007), term-structured yield curves (Kargin & Onatski 2008), spectrometry data (Reiss & Ogden 2007), or one of the many applications described by Ramsay & Silverman (2002).”
Penalized Functional Regression (2011, positive): “The third method, FPCRR (Reiss and Ogden 2007), first projects the random functions Xi(t) onto a B-spline basis and then performs a principal components analysis on the projection XB.”
Potential applications of functional data analysis in chemometrics (2008, methodology): “In this case variable selection techniques such as a forward-backward procedure [21] or a further dimensionality reduction by performing PCR or PLS on the B-spline regression coefficients [23] might be good options which have to be further investigated.”
Methodology and theory for partial least squares applied to functional data (2012, methodology): “It includes, for example, work by Cai and Hall (2006), Reiss and Ogden (2007), Apanasovich and Goldstein (2008), Cardot and Sarda (2008), Baillo (2009), Müller and Yao (2010), Wu, Fan and Müller (2010) and Yao and Müller (2010).”
Testing the Equality of Covariance Operators in Functional Samples (2011, background): “M E ] 2 point for many functional data analysis procedures, Reiss & Ogden (2007), Gervini (2008), Yao & Müller (2010), Gabrys et al. (2010) are just a handful of illustrative references.”
The functional linear array model (2015, background): “…functional effect linearly as the scalar product of the functional predictor and a smooth coefficient function, in the context of linear models (e.g., Reiss and Ogden, 2007; James et al., 2009), generalized linear models (e.g., Marx and Eilers, 1999; Müller and Stadtmüller, 2005; Wood, 2011;…”
Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data (2006, background): “It is also common to represent the spectra in terms of basis functions as B-Splines or wavelets [22, 4, 26] before applying regression techniques [32, 36].”