Statistical inference for partially linear additive spatial autoregressive models

Abstract

In this paper, a class of partially linear additive spatial autoregressive models (PLASARM) is studied. With the nonparametric functions approximated by basis functions, we propose a generalized method of moments estimator for PLASARM. Under mild conditions, we obtain the asymptotic normality for the finite parametric vector and the optimal convergence rate for nonparametric functions. In order to make statistical inference for parametric component, we propose the estimator for asymptotic covariance matrix of the parameter estimator and establish the asymptotic properties for the resulting estimators. Finite sample performance of the proposed method is assessed by Monte Carlo simulation studies, and the developed methodology is illustrated by an analysis of the Boston housing price data.