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Estimation in Partial Functional Linear Spatial Autoregressive Model

Author

Listed:
  • Yuping Hu

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Siyu Wu

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Sanying Feng

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
    Henan Key Laboratory of Financial Engineering, Zhengzhou University, Zhengzhou 450001, China)

  • Junliang Jin

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

Abstract

Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when response variables are dependence spatial variables. In this paper, we introduce a new partial functional linear spatial autoregressive model which explores the relationship between a scalar dependence spatial response variable and explanatory variables containing both multiple real-valued scalar variables and a function-valued random variable. By means of functional principal components analysis and the instrumental variable estimation method, we obtain the estimators of the parametric component and slope function of the model. Under some regularity conditions, we establish the asymptotic normality for the parametric component and the convergence rate for slope function. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies.

Suggested Citation

  • Yuping Hu & Siyu Wu & Sanying Feng & Junliang Jin, 2020. "Estimation in Partial Functional Linear Spatial Autoregressive Model," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1680-:d:422575
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    References listed on IDEAS

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
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    5. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
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