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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (9): 14-22.doi: 10.6040/j.issn.1671-9352.0.2024.354

• • 上一篇    

函数型互补双对数回归模型的局部稀疏估计

高海燕1,2,赵静娴1   

  1. 1.兰州财经大学统计与数据科学学院, 甘肃 兰州 730020;2.甘肃省数字经济与社会计算科学重点实验室, 甘肃 兰州 730020
  • 发布日期:2026-09-30
  • 作者简介:高海燕(1980— ),女,教授,博士生导师,博士,研究方向为复杂数据分析、聚类分析. E-mail:gaohy_54@sina.com
  • 基金资助:
    国家社会科学基金资助项目(19XTJ002,21BTJ042);全国统计科学研究重点项目(2025LZ007);甘肃省自然科学基金资助项目(23JRRA1186);甘肃省高校青年博士支持项目(2025QB-058)

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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摘要： 为有效识别标量响应变量和函数型协变量中的系数函数零子区域,提出一种稀疏函数型互补双对数回归模型(sparse functional complementary log-log regression, SFCLR)。该模型利用B样条基函数的紧支撑性,结合函数型数据的光滑处理技术和L1稀疏正则化策略,采用Newton-Raphson算法优化惩罚似然函数,从而实现局部稀疏估计。在常用函数和拉曼光谱数据上的数值模拟结果表明,SFCLR模型不仅能够有效识别系数函数的零值区域,还在非零系数区域生成连续平滑的估计值。同时,在Tecator脂肪数据集上的实证分析表明,通过SFCLR模型筛选出对肥胖特征判定具有显著贡献的波长区间,进一步验证该模型的有效性。

关键词: 函数型互补双对数回归模型, Newton-Raphson算法, 稀疏正则化, 惩罚似然

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

中图分类号: 

  • O212
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