Optimal sufficient dimension reduction for the conditional mean in multivariate regression

Yoo, Jae Keun; Cook, R. Dennis

doi:10.1093/biomet/asm003

Cited by 31 publications

(38 citation statements)

References 18 publications

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“…. , min(p, q) for estimating d. The applications of MDFs in various dimension reduction methods can be found in Cook (2007), Cook and Ni (2005), Cook and Zhang (2014), Ni and Cook (2007), Lee and Yoo (2014), Wen (2010), Yoo (2013), Yoo and Cook (2007) and Yoo and Lee (2011).…”

Section: Introductionmentioning

confidence: 99%

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A theoretical note on optimal sufficient dimension reduction with singularity

Yoo

2015

Statistics & Probability Letters

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Section: Introductionmentioning

confidence: 99%

“…Here we investigate two popular SDR methods for constructing the asymptotic covariance matrix ; (1) the sliced inverse regression method (SIR; Li, 1991) and (2) the ordinary least squares method (OLS; Yoo and Cook, 2007). For simplicity, we define = cov(X) and…”

Section: Introductionmentioning

confidence: 99%

A theoretical note on optimal sufficient dimension reduction with singularity

Yoo

2015

Statistics & Probability Letters

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“…Note that Yoo (2009) analyzed the variables x (1) , x (2) and x (3) while Cook (2009) focused on some increasing functions of these variables and Cook and Setodji (2003) …”

Section: Minneapolis Elementary Schools Datamentioning

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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“…Cook and Li (2002) investigated possible approaches to inferring about the central mean subspace when Y is univariate. Cook and Setodji (2003), Li et al (2003), Yoo and Cook (2007) studied estimation methods for the multivariate central mean subspace. Their works are not applicable to the estimation of the central subspace and are beyond the scope of this paper.…”

Section: Predictormentioning

confidence: 99%

A minimum discrepancy approach to multivariate dimension reduction via $k$-means inverse regression

Wen

Setodji

Adekpedjou

2009

Statistics and Its Interface

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We proposed a new method to estimate the intra-cluster adjusted central subspace for regressions with multivariate responses. Following Setodji and Cook (2004), we made use of the k-means algorithm to cluster the observed response vectors. Our method was designed to recover the intracluster information and outperformed previous method with respect to estimation accuracies on both the central subspace and its dimension. It also allowed us to test the predictor effects in a model-free approach. Simulation and a real data example were given to illustrate our methodology.

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Optimal sufficient dimension reduction for the conditional mean in multivariate regression

Cited by 31 publications

References 18 publications

A theoretical note on optimal sufficient dimension reduction with singularity

A theoretical note on optimal sufficient dimension reduction with singularity

A new sliced inverse regression method for multivariate response

A minimum discrepancy approach to multivariate dimension reduction via $k$-means inverse regression

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