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Spatial local linear quantile regression under association

Author

Listed:
  • Xu, Xin-Yi
  • Wang, Jiang-Feng
  • Hu, Kang
  • He, Shan
  • Xia, Yu

Abstract

This paper investigates the asymptotic properties of local linear quantile regression estimators for spatial data generated by strictly stationary and associated spatial processes {(Yi,Xi),i∈ZN}. We study local linear estimators for both the conditional quantile function qp(x) and its first-order partial derivatives. Under appropriate regularity conditions, we derive the Bahadur representation for these estimators, which is utilized to establish their joint asymptotic normality. To assess finite-sample performance, we conduct Monte Carlo simulations in a two-dimensional space (N=2). The results demonstrate the applicability of the proposed estimators and confirm the theoretical asymptotic properties.

Suggested Citation

  • Xu, Xin-Yi & Wang, Jiang-Feng & Hu, Kang & He, Shan & Xia, Yu, 2026. "Spatial local linear quantile regression under association," Statistics & Probability Letters, Elsevier, vol. 228(C).
    • Handle: RePEc:eee:stapro:v:228:y:2026:i:c:s0167715225002184
    DOI: 10.1016/j.spl.2025.110573
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    References listed on IDEAS

    as
    1. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    2. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    3. Chen Jia & Zhang Lixin & Li Degui, 2008. "Spatial local M-estimation under association," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(1), pages 11-29, January.
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