Statistical inference of varying-coefficient partial functional spatial autoregressive model

In this paper, based on spatial autoregression and partial functional linear regression, we introduce a new varying-coefficient partial functional spatial autoregressive model. The functional principal component analysis and B-spline are adopted to approximate the slope function and varying-coefficient functions respectively. Then, the instrumental variable method gives final estimators. Under some regular conditions, we further study the asymptotic normality of the parameter and the convergence rates of slope function and coefficient functions. Lastly, the finite sample performance of the proposed methodology is evaluated by simulation studies and a practical data example.