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On selection of spatial linear models for lattice data

Author

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  • Jun Zhu
  • Hsin‐Cheng Huang
  • Perla E. Reyes

Abstract

Summary. Spatial linear models are popular for the analysis of data on a spatial lattice, but statistical techniques for selection of covariates and a neighbourhood structure are limited. Here we develop new methodology for simultaneous model selection and parameter estimation via penalized maximum likelihood under a spatial adaptive lasso. A computationally efficient algorithm is devised for obtaining approximate penalized maximum likelihood estimates. Asymptotic properties of penalized maximum likelihood estimates and their approximations are established. A simulation study shows that the method proposed has sound finite sample properties and, for illustration, we analyse an ecological data set in western Canada.

Suggested Citation

  • Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:3:p:389-402
    DOI: 10.1111/j.1467-9868.2010.00739.x
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    3. 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.
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    Citations

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    Cited by:

    1. Jonathan Bradley & Noel Cressie & Tao Shi, 2015. "Rejoinder on: Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 54-60, March.
    2. Zhong, Yan & Sang, Huiyan & Cook, Scott J. & Kellstedt, Paul M., 2023. "Sparse spatially clustered coefficient model via adaptive regularization," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    3. Siddhartha Nandy & Chae Young Lim & Tapabrata Maiti, 2017. "Additive model building for spatial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 779-800, June.
    4. repec:cep:stiecm:/2013/562 is not listed on IDEAS
    5. Marwan Al-Momani & Abdulkadir A. Hussein & S. E. Ahmed, 2017. "Penalty and related estimation strategies in the spatial error model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(1), pages 4-30, January.
    6. Jonathan Bradley & Noel Cressie & Tao Shi, 2015. "Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 1-28, March.
    7. Al-Sulami, Dawlah & Jiang, Zhenyu & Lu, Zudi & Zhu, Jun, 2017. "Estimation for semiparametric nonlinear regression of irregularly located spatial time-series data," Econometrics and Statistics, Elsevier, vol. 2(C), pages 22-35.
    8. Liqian Cai & Tapabrata Maiti, 2020. "Variable selection and estimation for high‐dimensional spatial autoregressive models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 587-607, June.
    9. Javier Hidalgo & Myung Hwan Seo, 2013. "Specification For Lattice Processes," STICERD - Econometrics Paper Series 562, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Zhenyu Jiang & Nengxiang Ling & Zudi Lu & Dag Tj⊘stheim & Qiang Zhang, 2020. "On bandwidth choice for spatial data density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 817-840, July.
    11. Kangning Wang, 2018. "Variable selection for spatial semivarying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 323-351, April.
    12. repec:esx:essedp:767 is not listed on IDEAS
    13. Hidalgo, Javier & Seo, Myung Hwan, 2015. "Specification Tests For Lattice Processes," Econometric Theory, Cambridge University Press, vol. 31(2), pages 294-336, April.
    14. Wenning Feng & Abdhi Sarkar & Chae Young Lim & Tapabrata Maiti, 2016. "Variable selection for binary spatial regression: Penalized quasi‐likelihood approach," Biometrics, The International Biometric Society, vol. 72(4), pages 1164-1172, December.
    15. Miryam S. Merk & Philipp Otto, 2022. "Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross‐sectional resampling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    16. Xuan Liu & Jianbao Chen, 2021. "Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    17. He Jiang, 2023. "Robust forecasting in spatial autoregressive model with total variation regularization," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 195-211, March.
    18. Trevor J. Hefley & Mevin B. Hooten & Ephraim M. Hanks & Robin E. Russell & Daniel P. Walsh, 2017. "The Bayesian Group Lasso for Confounded Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 42-59, March.

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