Sufficient Dimension Reduction via Distance Covariance

Sheng, Wenhui; Yin, Xiangrong

doi:10.1080/10618600.2015.1026601

Cited by 41 publications

(26 citation statements)

References 23 publications

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“…The S yjx maximizes I(B). Sheng and Yin (2016) used the distance covariance to find the S yjx by the following optimization problem, max…”

Section: Methods Based On Nonlinear Dependencementioning

confidence: 99%

“…The

S_{bold-italicy ∣ bold-italicx}

maximizes I ( B ). Sheng and Yin (2016) used the distance covariance to find the

S_{bold-italicy ∣ bold-italicx}

by the following optimization problem,

\max_{B^{⊤} Σ_{xx} B = I_{d_{0}}, 1 \leq d_{0} \leq p} V^{2} ((), B^{⊤} bold-italicx, bold-italicy) .

…”

Section: Forward Regression Approachmentioning

confidence: 99%

“…More recent approaches of SDR usually consider local features on both x and y . See for example Xia (2007) and Yin, Li, and Cook (2008), Ma and Zhu (2012), Kong and Xia (2014), Luo, Li, and Yin (2014), and Sheng and Yin (2016).…”

Section: Introductionmentioning

confidence: 99%

“…There are many ways to implement the localization. For example, the local smoothing (Xia, 2007; Xia et al, 2002), slicing (Li, 1991; Wang & Xia, 2008), functional transformation of Luo et al (2014) and others Sheng and Yin (2016). However, in terms of original motivation, we divide all the method into two categories: (slicing) inverse regression methods, and others, called forward regression methods.…”

Section: Introductionmentioning

confidence: 99%

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Advance of the sufficient dimension reduction

Hang

Xia

2020

WIREs Computational Stats

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The sufficient dimension reduction of Li has been seen a steady development in the past 30 years in both methodology and application. The main approaches can be categorized into two groups: The inverse regression methods and forward regression methods. In this survey, we briefly discuss advances of methods and present problems that needs further investigation in the second group. This article is categorized under: Statistical Models > Multivariate Models Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Models > Semiparametric Models

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“…The S yjx maximizes I(B). Sheng and Yin (2016) used the distance covariance to find the S yjx by the following optimization problem, max…”

Section: Methods Based On Nonlinear Dependencementioning

confidence: 99%

“…The

S_{bold-italicy ∣ bold-italicx}

maximizes I ( B ). Sheng and Yin (2016) used the distance covariance to find the

S_{bold-italicy ∣ bold-italicx}

by the following optimization problem,

\max_{B^{⊤} Σ_{xx} B = I_{d_{0}}, 1 \leq d_{0} \leq p} V^{2} ((), B^{⊤} bold-italicx, bold-italicy) .

…”

Section: Forward Regression Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Advance of the sufficient dimension reduction

Hang

Xia

2020

WIREs Computational Stats

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“…So, the dimension reduction method is widely applied in practice. See, ; Lansangan and Barrios (2017); Luo et al (2017); Yoshida (2017); Deng and Wang (2017); Sheng and Yin (2016); Zhou and Zhu (2016). The central subspace satisfying model (1.1) is equivalent to the conditional density function of Y |X being the same as that of Y |B τ X for all possible value of X and Y if the conditional density function of Y given X exists, i.e.,…”

Section: B J P S -Accepted Manuscriptmentioning

confidence: 99%

Dimension reduction based on conditional multiple index density function

Zhang¹,

He²,

Lü³

et al. 2018

Braz. J. Probab. Stat.

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In this paper, a dimension reduction method is proposed by using the first derivative of the conditional density function of response given predictors. To estimate the central subspace, we propose a direct methodology by taking expectation of the product of predictor and kernel function about response, which helps to capture the directions in the conditional density function. The consistency and asymptotic normality of the proposed estimation methodology are investigated. Furthermore, we conduct some simulations to evaluate the performance of our proposed method and compare with existing methods, and a real data set is analyzed for illustration.

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Sufficient dimension folding in regression via distance covariance for matrix‐valued predictors

Sheng

Yuan

2019

Statistical Analysis

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In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we propose a new method of local search to estimate the structural dimensions. Simulations and real data analysis support the efficiency and effectiveness of the proposed method.

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Sufficient Dimension Reduction via Distance Covariance

Abstract: In this supplement, section A, section B and section C provide detailed proofs for Proposition 3, Proposition 4 and Corollary 1 in the paper respectively.

Cited by 41 publications

References 23 publications

Advance of the sufficient dimension reduction

Advance of the sufficient dimension reduction

Dimension reduction based on conditional multiple index density function

Sufficient dimension folding in regression via distance covariance for matrix‐valued predictors

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