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Estimating functional single index models with compact support

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  • Yunlong Nie
  • Liangliang Wang
  • Jiguo Cao

Abstract

The functional single index models are widely used to describe the nonlinear relationship between a scalar response and a functional predictor. The conventional functional single index model assumes that the coefficient function is nonzero in the entire time domain. In other words, the functional predictor always has a nonzero effect on the response all the time. We propose a new compact functional single index model, in which the coefficient function is only nonzero in a subregion. We also propose an efficient method that can simultaneously estimate the nonlinear link function, the coefficient function and also the nonzero region of the coefficient function. Hence, our method can identify the region in which the functional predictor is related to the response. Our method is illustrated by an application example in which the total number of daily bike rentals is predicted based on hourly temperature data. The finite sample performance of the proposed method is investigated by comparing it to the conventional functional single index model in a simulation study

Suggested Citation

  • Yunlong Nie & Liangliang Wang & Jiguo Cao, 2023. "Estimating functional single index models with compact support," Environmetrics, John Wiley & Sons, Ltd., vol. 34(2), March.
    • Handle: RePEc:wly:envmet:v:34:y:2023:i:2:n:e2784
    DOI: 10.1002/env.2784
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    References listed on IDEAS

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    1. Jialiang Li & Chao Huang & Zhub Hongtu, 2017. "A Functional Varying-Coefficient Single-Index Model for Functional Response Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1169-1181, July.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
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    Cited by:

    1. Wesley S. Burr & Nathaniel K. Newlands & Andrew Zammit‐Mangion, 2023. "Environmental data science: Part 2," Environmetrics, John Wiley & Sons, Ltd., vol. 34(2), March.
    2. Salim Bouzebda, 2024. "Limit Theorems in the Nonparametric Conditional Single-Index U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 12(13), pages 1-81, June.
    3. Luca Aiello & Matteo Fontana & Alessandra Guglielmi, 2023. "Bayesian functional emulation of CO2 emissions on future climate change scenarios," Environmetrics, John Wiley & Sons, Ltd., vol. 34(8), December.

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