Sparse Sliced Inverse Regression via Lasso

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if , where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additiona...

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Vydáno v:Journal of the American Statistical Association Ročník 114; číslo 528; s. 1726 - 1739
Hlavní autoři: Lin, Qian, Zhao, Zhigen, Liu, Jun S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Taylor & Francis 02.10.2019
Taylor & Francis Group, LLC
Taylor & Francis Ltd
Témata:
Algorithms
Analysis of covariance
Convergence
Covariance matrix
Dimension reduction
Eigenvectors
High dimensional statistics
Minimax
Noise
Regression
Regression analysis
sample size
Signal to noise ratio
Sparsity
Statistical methods
Statistics
Theory and Methods
Theory of large deviation
variance covariance matrix
ISSN:0162-1459, 1537-274X, 1537-274X
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Shrnutí:For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if , where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from top eigenvectors of the estimated conditional covariance matrix, we introduce a simple Lasso regression method to obtain an estimate of the SDR space. The resulting algorithm, Lasso-SIR, is shown to be consistent and achieves the optimal convergence rate under certain sparsity conditions when p is of order , where λ is the generalized signal-to-noise ratio. We also demonstrate the superior performance of Lasso-SIR compared with existing approaches via extensive numerical studies and several real data examples. Supplementary materials for this article are available online.
Bibliografie:ObjectType-Article-1
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2018.1520115