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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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    Cited by:

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    2. 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.
    3. 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.
    4. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    5. Guochang Wang, 2017. "Dimension reduction in functional regression with categorical predictor," Computational Statistics, Springer, vol. 32(2), pages 585-609, June.
    6. 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.
    7. Linjuan Zheng & Beiting Liang & Guochang Wang, 2024. "Adaptive slicing for functional slice inverse regression," Statistical Papers, Springer, vol. 65(5), pages 3261-3284, July.
    8. 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.
    9. 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.
    10. 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.
    11. Bergsma, Wicher P, 2020. "Regression with I-priors," Econometrics and Statistics, Elsevier, vol. 14(C), pages 89-111.
    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.
    13. Bergsma, Wicher, 2020. "Regression with I-priors," LSE Research Online Documents on Economics 102136, London School of Economics and Political Science, LSE Library.
    14. Xu, Wenchao & Zhang, Xinyu & Liang, Hua, 2024. "Linearized maximum rank correlation estimation when covariates are functional," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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