JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (9): 35-48.doi: 10.6040/j.issn.1671-9352.0.2025.200

Previous Articles    

Variable selection of SCAD-L2 penalty for the partially linear additive higher-order spatial autoregressive model

HUANG Shi1, CHENG Suli1,2*, GUO Shengliang1   

  1. 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
    2. Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, Chongqing Technology and Business University, Chongqing 400067, China
  • Published:2026-09-30

PDF (PC)

13

Abstract: A SCAD-L2 penalized least squares method for partially linear additive higher-order spatial autoregressive models is proposed, which can simultaneously perform group variable selection and parameter estimation for higher-order spatial lag terms and linear explanatory variables. It is proved that the proposed variable selection method possesses sparseness and asymptotic normality. The Monte Carlo numerical simulation further confirmed the excellent properties of the SCAD-L2 method in small samples. Finally, the proposed approach is applied to the analysis of the Boston housing price dataset, and the results show that the average number of rooms and the proportion of lower-status population have a significant impact on Boston housing price.

Key words: variable selection, additive model, spatial autoregressive model, grouping effect

CLC Number: 

  • O212
[1] Tibshirani R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society: Series B(Methodological), 1996, 58: 267-288.
[2] Zou Hui. The adaptive lasso and its oracle properties[J]. Journal of the American Statistical Association, 2006, 101(476): 1418-1429.
[3] 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.
[4] Hou Dake, Zhou Wenli, Zhang Qiuxia, et al. A comparative study of different variable selection methods based on numerical simulation and empirical analysis[J]. PeerJ Computer Science, 2023, 9: e1522.
[5] Zeng Lingmin, Xie Jun. Group variable selection via SCAD-L2[J]. Statistics: A Journal of Theoretical and Applied Statistics, 2014, 48(1): 49-66.
[6] Fan Jianqing, Li Runze. New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis[J]. Journal of the American Statistical Association, 2004, 99(467): 710-723.
[7] 罗国旺, 吴密霞. 部分线性可加空间自回归模型在约束条件下的统计推断[J]. 数理统计与管理, 2020, 39(6): 1000-1009. Luo Guowang, Wu Mixia. Statistical inference for partially linear additive spatial autoregressive models under constraints[J]. Journal of Applied Statistics and Management, 2020, 39(6): 1000-1009.
[8] Xie Tianfa, Cao Ruiyuan, Du Jiang. Variable selection for spatial autoregressive models with a diverging number of parameters[J]. Statistical Papers, 2020, 61: 1125-1145.
[9] Liu Xuan, Chen Jianbao. Variable selection for the spatial autoregressive model with autoregressive disturbances[J]. Mathematics, 2021, 9(1448): 1-20.
[10] 廖军, 文丽, 尹建鑫. 高阶空间自回归模型的选择与平均估计[J]. 系统科学与数学, 2021, 41(5): 1400-1417. Liao Jun, Wen Li, Yin Jianxin. Selection and averaging estimation for higher-order spatial autoregressive models[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(5): 1400-1417.
[11] 程素丽, 雷洋. 高阶空间自回归模型的变量选择[J/OL]. 山西大学学报(自然科学版), 2024-11-29. https: //doi.org/10.13451/j.sxu.ns.2024131. Cheng Suli, Lei Yang. Variable selection for higher-order spatial autoregressive models[J/OL]. Journal of Shanxi University(Natural Science Edition), 2024-11-29. https: //doi.org/10.13451/j.sxu.ns. 2024131.
[12] Luo Guowang, Wu Mixia. Variable selection for semiparametric varying-coefficient spatial autoregressive models with a diverging number of parameters[J]. Communications in Statistics-Theory and Methods, 2021, 50(9): 2062-2079.
[13] 陈凤, 刘嘉慧. 半参数空间自回归变系数模型的统计推断[J]. 统计与决策, 2024, 40(4): 17-22. Chen Feng, Liu Jiahui. Statistical inference for semiparametric spatial autoregressive varying coefficient models[J]. Statistics and Decision, 2024, 40(4): 17-22.
[14] 李体政, 方可. 部分线性变系数空间自回归模型的惩罚轮廓拟最大似然方法[J]. 工程数学学报, 2024, 41(4): 659-676. Li Tizheng, Fang Ke. Penalized profile quasi-maximum likelihood method for partially linear varying coefficient spatial autoregressive models[J]. Chinese Journal of Engineering Mathematics, 2024, 41(4): 659-676.
[15] 程瑶瑶, 李体政. 部分线性空间自回归模型的惩罚最小二乘方法[J]. 工程数学学报, 2024, 41(2): 294-310. Cheng Yaoyao, Li Tizheng. Penalized least squares method for partially linear spatial autoregressive models[J]. Chinese Journal of Engineering Mathematics, 2024, 41(2): 294-310.
[16] Zhu Nenghui, You Jinhong, Xu Qunfang. Iterative adaptive robust variable selection in nonparametric additive models[J]. Chinese Journal of Applied Probability and Statistics, 2024, 40(2): 201-228.
[17] 李根, 邹国华, 张新雨. 模型选择方法综述[J]. 数理统计与管理, 2012, 31(4): 640-658. Li Gen, Zou Guohua, Zhang Xinyu. A review of model selection methods[J]. Journal of Applied Statistics and Management, 2012, 31(4): 640-658.
[18] Yang Yiping, Zhao Peixin, Wu Dongsheng. Robust variable selection with exponential squared loss for linear mixed-effects models[J]. Metrika, 2024, 88(7): 981-1007.
[19] Harrison D, Rubinfeld D L. Hedonic housing prices and the demand for clean air[J]. Journal of Environmental Economics and Management, 1978, 5(1): 81-102.
[20] Li Tizheng, Mei Changlin. Statistical inference on the parametric component in partially linear spatial autore-gressive models[J]. Communications in Statistics: Simulation and Computation, 2016, 45: 1991-2006.
[21] Li Dengkui, Mei Changlin, Wang Ning. Tests for spatial dependence and heterogeneity in spatially autoregressive varying coefficient models with application to Boston house price analysis[J]. Regional Science and Urban Economics, 2019, 79: 103470.
[22] Li Tizheng, Kang Xiaojuan. Variable selection of higher-order partially linear spatial autoregressive model with a diverging number of parameters[J]. Statistical Papers, 2022, 63(1): 243-285.
[1] WANG Guojing, LI Tao, ZHEN Jiebo, NIE Xiaoling, GONG Chaofan, WANG Yan. Generalized additive models for characterizing atmospheric mercury mass concentration variations in the coastal area of Qingdao in summer [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 133-142.
[2] WANG Xiu-li. Variable selection based on DP algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(9): 81-86.
[3] ZHANG Xian-you, LI Dong-xi. A Bayesian approach for variable selection using spike-and-slab prior distribution [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 84-93.
[4] GAN Xin-jun, YANG Wei-qiang. Weight of evidence method and credit risk control [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(12): 55-59.
[5] LI Feng1, LU Yi-qiang2. Asymptotics for the LASSO estimator for partially linear models [J]. J4, 2012, 47(3): 93-97.
[6] WANG Shu-yun1, SONG Yun-sheng2. Bayesian variable selection based on AIC criteria in linear models [J]. J4, 2010, 45(6): 43-45.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd