Marginal tests with sliced average variance estimation

Shao, Yongwu; Cook, R. Dennis; Weisberg, Sanford

doi:10.1093/biomet/asm021

Cited by 52 publications

(56 citation statements)

References 18 publications

(14 reference statements)

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“…,γ p ) are the eigenvectors corresponding to the last (p − m) smallest eigenvalues ofM S AV E . Test statistics and their asymptotic distributions (Shao et al, 2007) …”

Section: Sliced Average Variance Estimationmentioning

confidence: 99%

Tutorial: Methodologies for sufficient dimension reduction in regression

Yoo

2016

Communications for Statistical Applications and Methods

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In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central k thmoment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.

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“…,γ p ) are the eigenvectors corresponding to the last (p − m) smallest eigenvalues ofM S AV E . Test statistics and their asymptotic distributions (Shao et al, 2007) …”

Section: Sliced Average Variance Estimationmentioning

confidence: 99%

Tutorial: Methodologies for sufficient dimension reduction in regression

Yoo

2016

Communications for Statistical Applications and Methods

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“…Apart from the original works of SIR, SAVE, pHd and POLS, general results regarding their test statistics are presented in Bura and Cook (2001), Shao et al (2007), Cook (1998) and Yoo (2013a) in the order; however, there exists big time gap between the original works and the derivation of the null distributions. Before the general results, a permutation test has been commonly adopted and will be discussed in the next subsection.…”

Section: Dimension Estimation In Sufficient Dimension Reductionmentioning

confidence: 99%

A Note on Bootstrapping in Sufficient Dimension Reduction

Yoo

Jeong

2015

CSAM

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A permutation test is the popular and attractive alternative to derive asymptotic distributions of dimension test statistics in sufficient dimension reduction methodologies; however, recent studies show that a bootstrapping technique also can be used. We consider two types of bootstrapping dimension determination, which are partial and whole bootstrapping procedures. Numerical studies compare the permutation test and the two bootstrapping procedures; subsequently, real data application is presented. Considering two additional bootstrapping procedures to the existing permutation test, one has more supporting evidence for the dimension estimation of the central subspace that allow it to be determined more convincingly.

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“…For an illustration purpose, the Swiss banknote data analyzed in Shao et al (SCW;2007) was considered. In the data, the following seven variables were used.…”

Section: Data Analysis -Swiss Banknote Datamentioning

confidence: 99%

Method-Free Permutation Predictor Hypothesis Tests in Sufficient Dimension Reduction

Lee¹,

Oh²,

Yoo³

2013

Communications for Statistical Applications and Methods

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In this paper, we propose method-free permutation predictor hypothesis tests in the context of sufficient dimension reduction. Different from an existing method-free bootstrap approach, predictor hypotheses are evaluated based on p-values; therefore, usual statistical practitioners should have a potential preference. Numerical studies validate the developed theories, and real data application is provided.

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Marginal tests with sliced average variance estimation

Cited by 52 publications

References 18 publications

Tutorial: Methodologies for sufficient dimension reduction in regression

Tutorial: Methodologies for sufficient dimension reduction in regression

A Note on Bootstrapping in Sufficient Dimension Reduction

Method-Free Permutation Predictor Hypothesis Tests in Sufficient Dimension Reduction

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