Variable selection for spatial autoregressive models with a diverging number of parameters

  • Tianfa Xie
  • Ruiyuan CaoEmail author
  • Jiang Du
Regular Article


Variable selection has played a fundamental role in regression analysis. Spatial autoregressive model is a useful tool in econometrics and statistics in which context variable selection is necessary but not adequately investigated. In this paper, we consider conducting variable selection in spatial autoregressive models with a diverging number of parameters. Smoothly clipped absolute deviation penalty is considered to obtain the estimators. Moreover the dimension of the covariates are allowed to vary with sample size. In order to attenuate the bias caused by endogeneity, instrumental variable is adopted in the estimation procedure. The proposed method can do parametric estimation and variable selection simultaneously. Under mild conditions, we establish the asymptotic and oracle property of the proposed estimators. Finally, the performance of the proposed estimation procedure is examined via Monte Carlo simulation studies and a data set from a Boston housing price is analyzed as an illustrative example.


Spatial autoregressive models Variable selection Instrumental variable Oracle property 

Mathematics Subject Classification

62G08 62G20 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Applied SciencesBeijing University of TechnologyBeijingChina

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