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Series expansion for functional sufficient dimension reduction

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  • Lian, Heng
  • Li, Gaorong

Abstract

Functional data are infinite-dimensional statistical objects which pose significant challenges to both theorists and practitioners. Both parametric and nonparametric regressions have received attention in the functional data analysis literature. However, the former imposes stringent constraints while the latter suffers from logarithmic convergence rates. In this article, we consider two popular sufficient dimension reduction methods in the context of functional data analysis, which, if desired, can be combined with low-dimensional nonparametric regression in a later step. In computation, predictor processes and index vectors are approximated in finite dimensional spaces using the series expansion approach. In theory, the basis used can be either fixed or estimated, which include both functional principal components and B-spline basis. Thus our study is more general than previous ones. Numerical results from simulations and a real data analysis are presented to illustrate the methods.

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  • Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:150-165
    DOI: 10.1016/j.jmva.2013.10.019
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    1. Benoît Liquet & Jérôme Saracco, 2012. "A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches," Computational Statistics, Springer, vol. 27(1), pages 103-125, March.
    2. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    3. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    4. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    5. Liping Zhu & Tao Wang & Lixing Zhu & Louis Ferré, 2010. "Sufficient dimension reduction through discretization-expectation estimation," Biometrika, Biometrika Trust, vol. 97(2), pages 295-304.
    6. 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.
    7. Wong, Heung & Zhang, Riquan & Ip, Wai-cheung & Li, Guoying, 2008. "Functional-coefficient partially linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 278-305, February.
    8. Gramacy, Robert B & Lee, Herbert K. H, 2008. "Bayesian Treed Gaussian Process Models With an Application to Computer Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1119-1130.
    9. 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.
    10. Zhu, Li-Ping & Zhu, Li-Xing & Feng, Zheng-Hui, 2010. "Dimension Reduction in Regressions Through Cumulative Slicing Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1455-1466.
    11. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
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    Cited by:

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    2. Allam, Abdelaziz & Mourid, Tahar, 2019. "Optimal rate for covariance operator estimators of functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 130-137.
    3. 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.
    4. Wang, Guochang & Zhou, Yan & Feng, Xiang-Nan & Zhang, Baoxue, 2015. "The hybrid method of FSIR and FSAVE for functional effective dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 64-77.
    5. Bergsma, Wicher P, 2020. "Regression with I-priors," Econometrics and Statistics, Elsevier, vol. 14(C), pages 89-111.
    6. Yuping Hu & Siyu Wu & Sanying Feng & Junliang Jin, 2020. "Estimation in Partial Functional Linear Spatial Autoregressive Model," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    7. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    8. Bergsma, Wicher, 2020. "Regression with I-priors," LSE Research Online Documents on Economics 102136, London School of Economics and Political Science, LSE Library.
    9. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    10. Guochang Wang, 2017. "Dimension reduction in functional regression with categorical predictor," Computational Statistics, Springer, vol. 32(2), pages 585-609, June.
    11. Lili Xia & Tingyu Lai & Zhongzhan Zhang, 2023. "An Adaptive-to-Model Test for Parametric Functional Single-Index Model," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    12. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.

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