JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (9): 14-22.doi: 10.6040/j.issn.1671-9352.0.2024.354

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Local sparse estimation of functional complementary log-log regression model

GAO Haiyan1,2, ZHAO Jingxian1   

  1. 1. School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, Gansu, China;
    2. Key Laboratory of Digital Economy and Social Computing Science, Gansu Province, Lanzhou 730020, Gansu, China
  • Published:2026-09-30

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Abstract: A sparse functional complementary log-log regression model(SFCLR)is proposed to effectively identify the zero sub-regions of the coefficient function in scalar response variables and functional covariates. The model leverages the compact support property of B-spline basis functions, integrates smoothing techniques for functional data with sparse regularization strategies, and utilizes the Newton-Raphson algorithm to optimize the penalized likelihood function, thereby achieving local sparse estimation. Numerical simulations based on common functions and Raman spectroscopy data demonstrate that the SFCLR model not only successfully identifies zero regions of coefficient functions but also produces continuous and smooth estimates in non-zero coefficient regions. Additionally, an empirical analysis using the Tecator fat dataset reveals that the SFCLR model can identify wavelength intervals that significantly contribute to determining obesity characteristics, further validating the models effectiveness.

Key words: functional complementary log-log regression model, Newton-Raphson algorithm, sparse regularization, penalized likelihood

CLC Number: 

  • O212
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