Abstract

In this paper we propose a model that generalizes some of the most popular choices in spatial linear
modeling, such as the SAR and MESS models. Our idea builds on their representation as link functions
applied to a spatial weight W, corresponding to the uniform and exponential distributions, respectively. By
allowing for more general families of distribution functions, one can encompass both models and capture
different spatial patterns. We provide some insights into the difference between specifications, with emphasis
on advantages and shortcomings as well as on interpretation of the parameters and correspondences between
models. By exploiting the possibility to obtain a formal power series representation of the link family, we
define the quasi maximum likelihood estimator and study its asymptotic properties under Gaussian and
non-Gaussian errors.

Based on a joint work with Andrea Martinelli, Department of Science and High Technology, Insubria University