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Robust functional sliced inverse regression

Author

Listed:
  • Guochang Wang

    (Jinan University)

  • Jianjun Zhou

    (Yunnan University)

  • Wuqing Wu

    (Renmin University of China)

  • Min Chen

    (Chinese Academy of Sciences)

Abstract

Functional data are infinite-dimensional statistical objects which pose significant challenges to both theorists and practitioners. To avoid the stringent constraints for parametric methods and low convergence rate for nonparametric methods, many functional dimension reduction methods have received attention in the functional data analysis literature, which, if desired, can be combined with low dimensional nonparametric regression in a later step. However, as far as we know that all of the functional dimension reduction methods are based on the classical estimates of the first and second moments of the data, and therefore sensitive to outliers. In the present paper, we propose a robust functional dimension reduction method by replacing the classical estimates with robust ones in the functional sliced inverse regression (FSIR). This leads to procedures which maintain the clever estimation scheme of the original FSIR method but can cope better with outliers. A comparison with FSIR is also made through simulation studies to show the robustness of the robust functional sliced inverse regression (RFSIR). As applications, the Orange juice data and the Tecator data are analyzed by using the proposed RFSIR method.

Suggested Citation

  • Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0695-x
    DOI: 10.1007/s00362-015-0695-x
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    References listed on IDEAS

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    1. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.
    2. Zhu, Hongxiao & Brown, Philip J. & Morris, Jeffrey S., 2011. "Robust, Adaptive Functional Regression in Functional Mixed Model Framework," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1167-1179.
    3. F. Ferraty & P. Hall & P. Vieu, 2010. "Most-predictive design points for functional data predictors," Biometrika, Biometrika Trust, vol. 97(4), pages 807-824.
    4. L. A. Prendergast, 2005. "Influence Functions for Sliced Inverse Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 385-404, September.
    5. Aneiros, Germán & Vieu, Philippe, 2014. "Variable selection in infinite-dimensional problems," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 12-20.
    6. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    7. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    8. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    9. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    10. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    11. Fang Yao & Hans-Georg Müller, 2010. "Functional quadratic regression," Biometrika, Biometrika Trust, vol. 97(1), pages 49-64.
    12. Pallavi Sawant & Nedret Billor & Hyejin Shin, 2012. "Functional outlier detection with robust functional principal component analysis," Computational Statistics, Springer, vol. 27(1), pages 83-102, March.
    13. Maronna, Ricardo A. & Yohai, Victor J., 2013. "Robust functional linear regression based on splines," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 46-55.
    14. Cook, R. Dennis & Forzani, Liliana, 2009. "Likelihood-Based Sufficient Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 197-208.
    15. Zhu, Li-Xing & Ohtaki, Megu & Li, Yingxing, 2007. "On hybrid methods of inverse regression-based algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2621-2635, February.
    16. Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
    17. Ningning Xia & Zhidong Bai, 2015. "Functional CLT of eigenvectors for large sample covariance matrices," Statistical Papers, Springer, vol. 56(1), pages 23-60, February.
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    Cited by:

    1. Guochang Wang & Beiting Liang & Hansheng Wang & Baoxue Zhang & Baojian Xie, 2021. "Dimension reduction for functional regression with a binary response," Statistical Papers, Springer, vol. 62(1), pages 193-208, February.
    2. Huiwen Wang & Zhichao Wang & Shanshan Wang, 2021. "Sliced inverse regression method for multivariate compositional data modeling," Statistical Papers, Springer, vol. 62(1), pages 361-393, February.
    3. Tang Qingguo & Bian Minjie, 2021. "Estimation for functional linear semiparametric model," Statistical Papers, Springer, vol. 62(6), pages 2799-2823, December.
    4. Tao Zhang & Zhiwen Wang & Yanling Wan, 2021. "Functional test for high-dimensional covariance matrix, with application to mitochondrial calcium concentration," Statistical Papers, Springer, vol. 62(3), pages 1213-1230, June.
    5. Eliana Christou, 2020. "Robust dimension reduction using sliced inverse median regression," Statistical Papers, Springer, vol. 61(5), pages 1799-1818, October.

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