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Estimation and inference in functional single-index models

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  • Shujie Ma

Abstract

We propose a functional single-index model (FSiM) to study the link between a scalar response variable and multiple functional predictors, in which the mean of the response is related to the linear predictors via an unknown link function. The FSiM serves as a good tool for dimension reduction in regression with multiple predictors and it is more flexible than functional linear models. Assuming that the functional predictors are observed at discrete points, we use B-spline basis functions to estimate the slope functions and the link function based on the least-squares criterion, and propose an iterative estimating procedure. Moreover, we provide uniform convergence rates of the proposed spline estimators in the FSiM, and construct asymptotic simultaneous confidence bands for the slope functions for inference. Our proposed method is illustrated by simulation studies and by an analysis of a diffusion tensor imaging data application. Copyright The Institute of Statistical Mathematics, Tokyo 2016

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  • Shujie Ma, 2016. "Estimation and inference in functional single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 181-208, February.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:1:p:181-208
    DOI: 10.1007/s10463-014-0488-3
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    Cited by:

    1. Zhiqiang Jiang & Zhensheng Huang & Jing Zhang, 2023. "Functional single-index composite quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 595-603, July.
    2. Yuyan Wang & Akhgar Ghassabian & Bo Gu & Yelena Afanasyeva & Yiwei Li & Leonardo Trasande & Mengling Liu, 2023. "Semiparametric distributed lag quantile regression for modeling time‐dependent exposure mixtures," Biometrics, The International Biometric Society, vol. 79(3), pages 2619-2632, September.
    3. Zi Ye & Giles Hooker, 2020. "Local quadratic estimation of the curvature in a functional single index model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1307-1338, December.
    4. Silvia Novo & Germán Aneiros & Philippe Vieu, 2021. "Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 481-504, June.
    5. Novo, Silvia & Aneiros, Germán & Vieu, Philippe, 2021. "A kNN procedure in semiparametric functional data analysis," Statistics & Probability Letters, Elsevier, vol. 171(C).
    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. Sudaraka Tholkage & Qi Zheng & Karunarathna B. Kulasekera, 2022. "Conditional Kaplan–Meier Estimator with Functional Covariates for Time-to-Event Data," Stats, MDPI, vol. 5(4), pages 1-17, November.
    8. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.

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