Statistical Inference Spatial Econometric Model

This note studies the existence and uniqueness of quasi-maximum likelihoodestimator for mixed regressive, spatial autoregression model with continuouslydistributed response vector. Under very mild condition that n rank （X_n）+1（n isthe sample size andX nis the n pconstant matrix of regressors）, we show thatthe quasi-likelihood function has exactly one maximum with probability one in theparameter space. If n rank （X_n）+1andX nhas full column rank, then the QMLEof（β, ρ,σ₂）exists and is unique with probability one.In order to detect the influential points and outliers, this study derives thedetection vector based on the first order derivative for the mixed autoregressivemodel. Simulation study show that both outliers and influential observations can beidentified by the proposed instrument. Meanwhile, our method can effectively avoidthe smearing and masking effect, which is usually encountered and difficult to handle.As the application, the paper analyzes a real data to illustrate the conclusions are veryreliable and practical.