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Robust functional sliced inverse regression

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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.

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Acknowledgments

We are grateful to the referees and the editors for their constructive remarks and careful reading of a previous version of the manuscript, which helped to improve the quality of the paper. Min Chen’s work was supported by the National Natural Science Foundation of China (No. 11371354), Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences, Beijing 100190, China (Grant No. 2008DP173182) and National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China. Guochang Wang’s work was supported by Project funded by China Postdoctoral Science Foundation (2013M541060), the National Science Foundation of China (No.11271064) and the Fundamental Research Funds for the Central Universities(12615304). Wuqing Wu’s work was supported by National Natural Science Foundation of China(Grant No.71003100), Supported by the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (No.11XNK027). Jianjun Zhou’s work was supported by the National Nature Science Foundation of China (Grant No. 11301464) and the Scientific Research Foundation of Yunnan Provincial Department of Education (No. 2013Y360).

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Authors and Affiliations

  1. College of Economics, Jinan University, Guangzhou, 510632, China

    Guochang Wang

  2. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, China

    Jianjun Zhou

  3. School of Business, Renmin University of China, Beijing, 100872, China

    Wuqing Wu

  4. Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190, China

    Min Chen

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  1. Guochang Wang
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  2. Jianjun Zhou
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  4. Min Chen
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Correspondence to Guochang Wang.

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Wang, G., Zhou, J., Wu, W. et al. Robust functional sliced inverse regression. Stat Papers 58, 227–245 (2017). https://doi.org/10.1007/s00362-015-0695-x

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  • DOI: https://doi.org/10.1007/s00362-015-0695-x

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