<p>In this paper, we focus on estimation and inference of high-dimensional partially linear spatial autoregressive models when a linear constraint on regression coefficients is available. Based on series method, two-stage least squares method and Lagrange multiplier method, we obtain constrained estimators of the parametric component, nonparametric component and error variance, and study their asymptotic properties. Moreover, we construct a Wald statistic to test validity of some linear constraint on the regression coefficients, and derive its asymptotic distribution under null and alternative hypotheses. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimation and testing methods, and simulation results show that the proposed constrained estimators outperform the unconstrained estimators and the proposed testing method is of reasonable size and satisfactory power. A real data example is provided to demonstrate application of the proposed estimation and testing methods.</p>

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Estimation and inference of high-dimensional partially linear spatial autoregressive models with linear constraints

  • Tizheng Li,
  • Ting Liu,
  • Xiangyi Zhang

摘要

In this paper, we focus on estimation and inference of high-dimensional partially linear spatial autoregressive models when a linear constraint on regression coefficients is available. Based on series method, two-stage least squares method and Lagrange multiplier method, we obtain constrained estimators of the parametric component, nonparametric component and error variance, and study their asymptotic properties. Moreover, we construct a Wald statistic to test validity of some linear constraint on the regression coefficients, and derive its asymptotic distribution under null and alternative hypotheses. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimation and testing methods, and simulation results show that the proposed constrained estimators outperform the unconstrained estimators and the proposed testing method is of reasonable size and satisfactory power. A real data example is provided to demonstrate application of the proposed estimation and testing methods.