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A Note on Sliced Inverse Regression with Regularizations

Author

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  • C. Bernard‐Michel
  • L. Gardes
  • S. Girard

Abstract

Summary In Li and Yin (2008, Biometrics64, 124–131), a ridge SIR estimator is introduced as the solution of a minimization problem and computed thanks to an alternating least‐squares algorithm. This methodology reveals good performance in practice. In this note, we focus on the theoretical properties of the estimator. It is shown that the minimization problem is degenerated in the sense that only two situations can occur: Either the ridge SIR estimator does not exist or it is zero.

Suggested Citation

  • C. Bernard‐Michel & L. Gardes & S. Girard, 2008. "A Note on Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(3), pages 982-984, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:982-984
    DOI: 10.1111/j.1541-0420.2008.01080.x
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    References listed on IDEAS

    as
    1. Lexin Li & Xiangrong Yin, 2008. "Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(1), pages 124-131, March.
    2. Cook, R. Dennis & Ni, Liqiang, 2005. "Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 410-428, June.
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    Cited by:

    1. Coudret, R. & Girard, S. & Saracco, J., 2014. "A new sliced inverse regression method for multivariate response," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 285-299.
    2. Lexin Li & Xiangrong Yin, 2008. "The authors replied as follows:," Biometrics, The International Biometric Society, vol. 64(3), pages 984-986, September.
    3. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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