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

Tianfa Xie, Ruiyuan Cao () and Jiang Du
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Tianfa Xie: Beijing University of Technology
Ruiyuan Cao: Beijing University of Technology
Jiang Du: Beijing University of Technology

Statistical Papers, 2020, vol. 61, issue 3, No 10, 1125-1145

Abstract: Abstract 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.

Keywords: Spatial autoregressive models; Variable selection; Instrumental variable; Oracle property; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s00362-018-0984-2

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