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On selection of spatial linear models for lattice data

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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.

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  • 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. 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.
    3. 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.
    4. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. repec:cep:stiecm:/2013/562 is not listed on IDEAS
    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. 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.
    8. 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.
    9. 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.
    10. Hidalgo, Javier & Seo, Myung Hwan, 2015. "Specification Tests For Lattice Processes," Econometric Theory, Cambridge University Press, vol. 31(2), pages 294-336, April.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. repec:esx:essedp:767 is not listed on IDEAS
    16. 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.
    17. 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.
    18. Xuan Liu & Jianbao Chen, 2021. "Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances," Mathematics, MDPI, vol. 9(12), pages 1-20, June.

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