Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors

This paper explores the estimators of parameters for a partially linear single-index spatial model which has measurement errors in all variables. We propose an efficient methodology to estimate our model by combining a local-linear smoother based Pseudo- \(\theta \) $\theta$ algorithm, simulation-extrapolation (SIMEX) algorithm, the estimation equation and the estimation method for profile maximum likelihood. Under some regular conditions, we derive the asymptotic properties of the link function and unknown estimators. Some simulations indicate our estimation method performs well. Finally, we apply our method to a real data set of Boston Housing Price. The result shows that our model fits the data set well.