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A robust inverse regression estimator

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  • Ni, Liqiang
  • Cook, R. Dennis

Abstract

A family of dimension reduction methods was developed by Cook and Ni [Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J. Amer. Statist. Assoc. 100, 410-428.] via minimizing a quadratic objective function. Its optimal member called the inverse regression estimator (IRE) was proposed. However, its calculation involves higher order moments of the predictors. In this article, we propose a robust version of the IRE that only uses second moments of the predictor for estimation and inference, leading to better small sample results.

Suggested Citation

  • Ni, Liqiang & Cook, R. Dennis, 2007. "A robust inverse regression estimator," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 343-349, February.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:3:p:343-349
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    References listed on IDEAS

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    1. Bura E. & Cook R.D., 2001. "Extending Sliced Inverse Regression: the Weighted Chi-Squared Test," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 996-1003, September.
    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. Yoo, Jae Keun, 2015. "A theoretical note on optimal sufficient dimension reduction with singularity," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 109-113.
    2. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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