Estimation of partially linear single-index spatial autoregressive model

In this paper, we first present partially linear single-index spatial autoregressive model and propose its profile maximum likelihood estimators (PMLE). Subsequently, consistency and asymptotic normality of the estimators for parameters and unknown link function are derived under some regular conditions. Thirdly, Monte Carlo simulations are used to investigate the performances of these estimators in finite sample cases. Finally, the proposed method is illustrated with the real data set of Boston Housing Price.