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Robust variable selection with exponential squared loss for partially linear spatial autoregressive models

Author

Listed:
  • Xiuli Wang

    (Shandong Normal University)

  • Jingchang Shao

    (Shandong Normal University)

  • Jingjing Wu

    (University of Calgary)

  • Qiang Zhao

    (Shandong Normal University)

Abstract

In this paper, we consider variable selection for a class of semiparametric spatial autoregressive models based on exponential squared loss (ESL). Using the orthogonal projection technique, we propose a novel orthogonality-based variable selection procedure that enables simultaneous model selection and parameter estimation, and identifies the significance of spatial effects. Under appropriate conditions, we show that the proposed procedure is consistent and the resulting estimator has oracle properties. Furthermore, some simulation studies and an analysis of the Boston housing price data are also carried out to examine the finite-sample performance of the proposed method.

Suggested Citation

  • Xiuli Wang & Jingchang Shao & Jingjing Wu & Qiang Zhao, 2023. "Robust variable selection with exponential squared loss for partially linear spatial autoregressive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(6), pages 949-977, December.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:6:d:10.1007_s10463-023-00870-w
    DOI: 10.1007/s10463-023-00870-w
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