Abstract
Sufficient dimension reduction (SDR) is known to be a powerful tool for achieving data reduction and data visualization in regression and classification problems. In this work, we study ultrahigh-dimensional SDR problems and propose solutions under a unified minimum discrepancy approach with regularization. When p grows exponentially with n, consistency results in both central subspace estimation and variable selection are established simultaneously for important SDR methods, including sliced inverse regression (SIR), principal fitted component (PFC), and sliced average variance estimation (SAVE). Special sparse structures of large predictor or error covariance are also considered for potentially better performance. In addition, the proposed approach is equipped with a new algorithm to efficiently solve the regularized objective functions and a new data-driven procedure to determine structural dimension and tuning parameters, without the need to invert a large covariance matrix. Simulations and a real data analysis are offered to demonstrate the promise of our proposal in ultrahigh-dimensional settings. Supplementary materials for this article are available online.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1277-1290 |
| Number of pages | 14 |
| Journal | Journal of the American Statistical Association |
| Volume | 114 |
| Issue number | 527 |
| DOIs | |
| State | Published - Jul 3 2019 |
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Keywords
- Central subspace
- Inverse regression
- Principal fitted component
- Sliced average variance estimation
- Sliced inverse regression
- Sparsity
Cite this
Sparse Minimum Discrepancy Approach to Sufficient Dimension Reduction with Simultaneous Variable Selection in Ultrahigh Dimension. / Qian, Wei; Ding, Shanshan; Cook, R. D.
In: Journal of the American Statistical Association, Vol. 114, No. 527, 03.07.2019, p. 1277-1290.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Sparse Minimum Discrepancy Approach to Sufficient Dimension Reduction with Simultaneous Variable Selection in Ultrahigh Dimension
AU - Qian, Wei
AU - Ding, Shanshan
AU - Cook, R. D
PY - 2019/7/3
Y1 - 2019/7/3
N2 - Sufficient dimension reduction (SDR) is known to be a powerful tool for achieving data reduction and data visualization in regression and classification problems. In this work, we study ultrahigh-dimensional SDR problems and propose solutions under a unified minimum discrepancy approach with regularization. When p grows exponentially with n, consistency results in both central subspace estimation and variable selection are established simultaneously for important SDR methods, including sliced inverse regression (SIR), principal fitted component (PFC), and sliced average variance estimation (SAVE). Special sparse structures of large predictor or error covariance are also considered for potentially better performance. In addition, the proposed approach is equipped with a new algorithm to efficiently solve the regularized objective functions and a new data-driven procedure to determine structural dimension and tuning parameters, without the need to invert a large covariance matrix. Simulations and a real data analysis are offered to demonstrate the promise of our proposal in ultrahigh-dimensional settings. Supplementary materials for this article are available online.
AB - Sufficient dimension reduction (SDR) is known to be a powerful tool for achieving data reduction and data visualization in regression and classification problems. In this work, we study ultrahigh-dimensional SDR problems and propose solutions under a unified minimum discrepancy approach with regularization. When p grows exponentially with n, consistency results in both central subspace estimation and variable selection are established simultaneously for important SDR methods, including sliced inverse regression (SIR), principal fitted component (PFC), and sliced average variance estimation (SAVE). Special sparse structures of large predictor or error covariance are also considered for potentially better performance. In addition, the proposed approach is equipped with a new algorithm to efficiently solve the regularized objective functions and a new data-driven procedure to determine structural dimension and tuning parameters, without the need to invert a large covariance matrix. Simulations and a real data analysis are offered to demonstrate the promise of our proposal in ultrahigh-dimensional settings. Supplementary materials for this article are available online.
KW - Central subspace
KW - Inverse regression
KW - Principal fitted component
KW - Sliced average variance estimation
KW - Sliced inverse regression
KW - Sparsity
UR - http://www.scopus.com/inward/record.url?scp=85055709008&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85055709008&partnerID=8YFLogxK
U2 - 10.1080/01621459.2018.1497498
DO - 10.1080/01621459.2018.1497498
M3 - Article
AN - SCOPUS:85055709008
VL - 114
SP - 1277
EP - 1290
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
SN - 0162-1459
IS - 527
ER -