Efficient Estimation of the SemiparametricSpatial Autoregressive Model

Efficient semiparametric and parametric estimates are developed for aspatial autoregressive model, containing nonstochastic explanatoryvariables and innovations suspected to be non-normal. The main stress ison the case of distribution of unknown, nonparametric, form, where seriesnonparametric estimates of the score function are employed in adaptiveestimates of parameters of interest. These estimates are as efficient asones based on a correct form, in particular they are more efficient thanpseudo-Gaussian maximum likelihood estimates at non-Gaussiandistributions. Two different adaptive estimates are considered. One entails astringent condition on the spatial weight matrix, and is suitable only whenobservations have substantially many "neighbours". The other adaptiveestimate relaxes this requirement, at the expense of alternative conditionsand possible computational expense. A Monte Carlo study of finite sampleperformance is included.