JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (9): 23-34.doi: 10.6040/j.issn.1671-9352.0.2024.309

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Sparse and robust estimation of longitudinal data regression models based on the exponential squared function

CHENG Yuhe1,2, ZHANG Bin1,2*   

  1. 1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, Guangxi, China;
    2. Key Laboratory of Interdisciplinary Research for Data Science, Guangxi Normal University, Guilin 541006, Guangxi, China
  • Published:2026-09-30

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Abstract: First, the exponential squared function is used to construct a new score function to achieve a robust estimation of the regression parameters. Second, the empirical likelihood function is penalized by the smoothly clipped absolute deviation, so that the mean and covariance matrix estimates simultaneously possess good statistical properties of sparsity and robustness. Additionally, a Newton-Raphson iterative algorithm for solving the model is provided. Finally, the asymptotic normality of the parameter estimators is proved, and the proposed method is compared with existing methods through numerical simulations, demonstrating superior performance in terms of robustness and sparsity across different covariance structures and error distributions.

Key words: longitudinal data model, robust estimation, empirical likelihood estimation, exponential squared function, sparsity

CLC Number: 

  • O212
[1] 汤宁, 宋秋月, 易东, 等. 医学纵向数据建模方法及其统计分析策略[J]. 中国卫生统计, 2019, 36(3): 441-444, 447. Tong Ning, Song Qiuyue, Yi Dong, et al. Medical longitudinal data modelling methods and their statistical analysis strategies[J]. China Health Statistics, 2019, 36(3): 441-444, 447.
[2] Owen A. Empirical likelihood ratio confidence intervals for a single functional[J]. Biometrika, 1988, 75(2): 237-249.
[3] Owen A. Empirical likelihood ratio confidence regions[J]. The Annals of Statistics, 1990, 18(1): 90-120.
[4] Pascal F, Harari-Kermadec H, Larzabal P. The empirical likelihood method applied to covariance matrix estimation[J]. Signal Processing, 2009, 90(2): 566-578.
[5] 袁进义, 杨宜平. 纵向数据下工具变量线性回归模型的经验似然推断[J]. 统计与决策, 2016, 32(19): 73-75. Yuan Jinyi, Yang Yiping. Empirical likelihood inference for instrumental variable linear regression models with longitudinal data[J]. Statistics and Decision, 2016, 32(19): 73-75.
[6] Chen Hong, Zhang Xin, Fang Yixin. Exponential square loss in random effects modeling for longitudinal data[J]. Biometrika, 2020, 107(3): 563-577.
[7] Wang Qing, Lin Yi, Zhang Shuang. Empirical likelihood in nonparametric longitudinal data models[J]. Journal of Nonparametric Statistics, 2021, 33(5): 829-846.
[8] 向亚云, 樊亚莉. 纵向数据下基于广义经验似然的有效自适应双稳健回归[J]. 应用概率统计, 2022, 38(5): 723-744. Xiang Yayun, Fan Yali. Efficient adaptive double-robust regression based on generalized empirical likelihood for longitudinal data[J]. Applied Probability and Statistics, 2022, 38(5): 723-744.
[9] 李颖, 周旋, 蒙惠芳, 等. 基于损失函数为指数平方形式的稳健logistic回归[J]. 海南大学学报(自然科学版), 2019, 37(4): 287-291. Li Ying, Zhou Xuan, Meng Huifang, et al. Robust logistic regression based on exponential squared loss function[J]. Journal of Hainan University(Natural Science Edition), 2019, 37(4): 287-291.
[10] Xu Liang, Liu Zhen. Exponential square loss for partial linear models in noisy longitudinal data[J]. Journal of the American Statistical Association, 2022, 117(538): 1254-1265.
[11] Fang Yixin, Chen Yiming, Zhang Tianyu. Robust dynamic modeling for longitudinal data using exponential square loss[J]. Computational Statistics & Data Analysis, 2023, 177: 107459.
[12] Huang J H, Liu N P, Pourahmadi M, et al. Covariance matrix selection and estimation via penalized normal likelihood[J]. Biometrika, 2012, 99(4): 973-984.
[13] Wang Huixia, Zhu Ji. Quantile regression in longitudinal data analysis[J]. Biometrics, 2021, 77(2): 458-470.
[14] Xu J, Mackenzie G. Modeling covariance structure in bivariate marginal models for longitudinal data[J]. Biometrika, 2022, 109(2): 291-303.
[15] Mao J H, Zhu Z Y, Fung W K. Joint estimation of mean-covariance model for longitudinal data with basis function approximations[J]. Computational Statistics & Data Analysis, 2011, 55(2): 983-992.
[16] Fan Jianqing, Li Runze. Variable selection via nonconcave penalized likelihood and its oracle properties[J]. Journal of the American Statistical Association, 2001, 96(456): 1348-1360.
[17] Zou Hui. The adaptive Lasso and its oracle properties[J]. Journal of the American Statistical Association, 2006, 101: 1418-1429.
[18] Tang Chengyu, Leng Chenlei. Penalized high-dimensional empirical likelihood[J]. Biometrika, 2010, 97(4): 905-920.
[19] Leng Chenlei, Tang Chenyu. Penalized empirical likelihood and growing dimensional general estimating equations[J]. Biometrika, 2012, 99: 703-716.
[20] Qin J, Lawless J. Empirical likelihood and general estimating equations[J]. The Annals of Statistics, 1994, 22: 300-325.
[21] Wang H S, Li R Z, Tsai C L. Tuning parameter selectors for the smoothly clipped absolute deviation method[J]. Biometrika, 2007, 94(3): 553-568.
[22] Zheng X Y, Fung W K, Zhu Z Y. Variable selection in robust joint mean and covariance model for longitudinal data analysis[J]. Statistica Sinica, 2014, 24(2): 515-531.
[23] Zheng X Y, Fung W K, Zhu Z Y. Robust estimation in joint mean-covariance regression model for longitudinal data[J]. Annals of the Institute of Statistical Mathematics, 2013, 65(4): 617-638.
[24] Qin Gouyou, Zhu Zhongyi. Robust estimation of mean and covariance for longitudinal data with dropouts[J]. Journal of Applied Statistics, 2015, 42(6): 1240-1254.
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