Smoothed Functional Inverse Regression

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Functional Data Analysis (2016, methodology): “…which was ﬁrst proposed for vector covariates as an oﬀ-shoot of sliced inverse regression (SIR) (Duan & Li 1991; Li 1991), and has been extended to functional data in Ferr´e & Yao (2003); Ferr´e & Yao (2005); Cook, Forzani & Yao (2010) and to longitudinal data in Jiang, Yu & Wang (2014).”
Nonparametric modelling for functional data: selected survey and tracks for future (2018, methodology): “Other semiparametric functional models are Projection Pursuit Regression [136,137], Slice Inverse Regression [138,139], and Partial Linear Regression [140–150].”
On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, unknown): “…1992), SIR, sliced average variance estimator (SAVE; Cook and Weisberg 1991; Cook and Critchley 2000), kernel inverse regression (Zhu and Fang 1996; Ferre and Yao 2005), structure adaptive estimator (Hristache, Juditsky, Polzehl, and Spokoiny 2001), iterative Hessian transformations (Cook and Li…”
Functional sliced inverse regression analysis (2003, methodology): “Another point is that, in Ferré and Yao (2003), we use the fact that G 1=2GeG 1=2 is a finite rank operator with the same sequence of eigenvectors as G1=2Gþe G 1=2; Ferré and Villa (2003) show the consistency of the estimators of the functions b even when Ge is no longer estimated by slicing but…”