Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias

Under flexible distributional assumptions, the adjusted quasi-maximum likelihood (adqmladqml) estimator for mixed regressive, spatial autoregressive model is studied in this paper. The proposed estimation method accommodates the extra uncertainty introduced by the unknown regression coefficients. Moreover, the explicit expressions of theoretical/feasible second-order-bias of the adqmladqml estimator are derived and the difference between them is investigated. The feasible second-order-bias corrected adqmladqml estimator is then designed accordingly for small sample setting. Extensive simulation studies are conducted under both normal and non-normal situations, showing that the quasi-maximum likelihood (qmlqml) estimator suffers from large bias when the sample size is relatively small in comparison to the number of regression coefficients and such bias can be effectively eliminated by the proposed adqmladqml estimation method. The use of the method is then demonstrated in the analysis of the Neighborhood Crimes Data.