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Using DAGs to identify the sufficient dimension reduction in the Principal Fitted Components model

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  • Szretter Noste, María Eugenia

Abstract

We identify the sufficient reduction for the Principal Fitted Components model under mild conditions which generalize those considered in previous works. We give a short proof of the main result based on the d-separation for directed acyclic graphs (DAGs), linking two areas that, to our knowledge, have not been linked before in statistics.

Suggested Citation

  • Szretter Noste, María Eugenia, 2019. "Using DAGs to identify the sufficient dimension reduction in the Principal Fitted Components model," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 317-320.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:317-320
    DOI: 10.1016/j.spl.2018.08.008
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    1. Efstathia Bura & Sabrina Duarte & Liliana Forzani, 2016. "Sufficient Reductions in Regressions With Exponential Family Inverse Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1313-1329, July.
    2. Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.
    3. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
    4. 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.
    5. Efstathia Bura & Liliana Forzani, 2015. "Sufficient Reductions in Regressions With Elliptically Contoured Inverse Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 420-434, March.
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    Cited by:

    1. Andrea Bergesio & María Eugenia Szretter Noste & Víctor J. Yohai, 2021. "A robust proposal of estimation for the sufficient dimension reduction problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 758-783, September.

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