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Simultaneous dimension reduction and variable selection in modeling high dimensional data

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  • Lansangan, Joseph Ryan G.
  • Barrios, Erniel B.

Abstract

High dimensional predictors in regression analysis are often associated with multicollinearity along with other estimation problems. These problems can be mitigated through a constrained optimization method that simultaneously induces dimension reduction and variable selection that also maintains a high level of predictive ability of the fitted model. Simulation studies show that the method may outperform sparse principal component regression, least absolute shrinkage and selection operator, and elastic net procedures in terms of predictive ability and optimal selection of inputs. Furthermore, the method yields reduced models with smaller prediction errors than the estimated full models from the principal component regression or the principal covariance regression.

Suggested Citation

  • Lansangan, Joseph Ryan G. & Barrios, Erniel B., 2017. "Simultaneous dimension reduction and variable selection in modeling high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 242-256.
    • Handle: RePEc:eee:csdana:v:112:y:2017:i:c:p:242-256
    DOI: 10.1016/j.csda.2017.03.015
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    References listed on IDEAS

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    1. Artur Klinger, 2001. "Inference in high dimensional generalized linear models based on soft thresholding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 377-392.
    2. Hugh Chipman & Hong Gu, 2005. "Interpretable dimension reduction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 969-987.
    3. Ian T. Jolliffe, 1982. "A Note on the Use of Principal Components in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 300-303, November.
    4. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    5. Reinhold Kosfeld & Jørgen Lauridsen, 2008. "Factor analysis regression," Statistical Papers, Springer, vol. 49(4), pages 653-667, October.
    6. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    7. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    8. Tze‐San Lee, 1987. "Optimum Ridge Parameter Selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(1), pages 112-118, March.
    9. Lisha Chen & Jianhua Z. Huang, 2012. "Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1533-1545, December.
    10. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    11. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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