Dimension reduction in functional regression with applications

Amato, Umberto; Antoniadis, Anestis; Feis, Italia De

doi:10.1016/j.csda.2004.12.007

Cited by 70 publications

(63 citation statements)

References 26 publications

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“…Regularized versions for SIR have been proposed for high-dimensional covariates, see for instance Zhu 6 et al (2006), Scrucca (2007), Li and Yin (2008), Bernard-Michel et al (2008). Amato et al (2006) developed an extension of SIR when x is a sampled function. Sparse SIR has been proposed by Li and Nachtsheim (2006).…”

Section: Univariate Sirmentioning

confidence: 99%

A new sliced inverse regression method for multivariate response

Coudret

Girard²,

Saracco³

2014

Computational Statistics & Data Analysis

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To cite this version:Abstract A semiparametric regression model of a q-dimensional multivariate response y on a p-dimensional covariate x is considered. A new approach is proposed based on sliced inverse regression (SIR) for estimating the effective dimension reduction (EDR) space without requiring a prespecified parametric model. The convergence at rate √ n of the estimated EDR space is shown. The choice of the dimension of the EDR space is discussed. Moreover, a way to cluster components of y related to the same EDR space is provided. Thus, the proposed multivariate SIR method can be used properly on each cluster instead of blindly applying it on all components of y. The numerical performances of multivariate SIR are illustrated on a simulation study. Applications to a remote sensing dataset and to the Minneapolis elementary schools data are also provided. Although the proposed methodology relies on SIR, it opens the door for new regression approaches with a multivariate response.They could be built similarly based on other reduction dimension methods.

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Section: Univariate Sirmentioning

confidence: 99%

A new sliced inverse regression method for multivariate response

Coudret

Girard²,

Saracco³

2014

Computational Statistics & Data Analysis

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“…The key of FSIR is the connection between the edr-space and the inverse regression curve given by the covariance operator of the inverse regression curve e . Indeed it is possible to prove under some mild assumptions (Amato et al, 2006) that the eigenvalue-eigenvector decomposition of the operator −1 R e permits to identify a basis for the edr-space. Unfortunately the inverse of R is not bounded, therefore we consider…”

Section: The Regression Modelmentioning

confidence: 99%

“…Convergence in probability of bothˆ R,N andˆ e,N to R and e can be found in (Amato et al, 2006). To estimate them accurately, we improve the conditioning ofˆ e,N applying a projector method before performing the spectral decomposition: letπ k N denote the orthogonal projector into the space spanned by the k N eigenvectors ofˆ e,N corresponding to the k N largest eigenvalues; we letˆ k N e,N =π k Nˆ e,Nπ k N .…”

Section: The Regression Modelmentioning

confidence: 99%

“…Functional Sliced Inverse Regression (FSIR) (Amato et al, 2006) is a statistical tool to reduce the dimensionality based on the Sliced Inverse Regression (SIR) (Li, 1991), that permits to deal with functional models. It generalizes the Principal Component Analysis (PCA) using inverse regression.…”

Section: The Regression Modelmentioning

confidence: 99%

“…The methodology is based on a suitable statistical dimension reduction technique, FSIR (Functional Sliced Inverse Regressions. FSIR (Amato et al, 2006) generalizes the well known Principal Component Analysis (PCA) (Jolliffe, 2002, e.g. ) or Empirical Orthogonal Function (EOF) approach (see the recent review on EOF regression methods by Serio et al, 2009) and allows one to deal with functional models.…”

Section: Introductionmentioning

confidence: 99%

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Technical Note: Functional sliced inverse regression to infer temperature, water vapour and ozone from IASI data

et al. 2009

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Abstract.A retrieval algorithm that uses a statistical strategy based on dimension reduction is proposed. The methodology and details of the implementation of the new algorithm are presented and discussed. The algorithm has been applied to high resolution spectra measured by the Infrared Atmospheric Sounding Interferometer instrument to retrieve atmospheric profiles of temperature, water vapour and ozone. The performance of the inversion strategy has been assessed by comparing the retrieved profiles to the ones obtained by colocating in space and time profiles from the European Centre for Medium-Range Weather Forecasts analysis.

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