A note on the existence and uniqueness of quasi-maximum likelihood estimators for mixed regressive, spatial autoregression models

This note studies the existence and uniqueness of quasi-maximum likelihood estimator for mixed regressive, spatial autoregression model with continuously distributed response vector. Under very mild conditions that n>rank(Xn)+1 (nn is the sample size and XnXn is the n×pn×p constant matrix of regressors), we show that the quasi-likelihood function has exactly one maximum with probability one in the parameter space.