Estimation in Partial Functional Linear Spatial Autoregressive Model

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.