On the Asymptotic Distribution of the Moran I Test Statistic with Applications

By far, the most popular test for spatial correlation is the one based on Moran's (1950) I test statistic. Despite this, the available results in the literature concerning the large sample distribution of this statistic are limited and have been derived under assumptions that do not cover many applications of interest. In this paper we first give a general result concerning the large sample distribution of Moran I type test statistic. We then apply this result to derive the large sample distribution of the Moran I test statistic for a variety of important models for which general spatial correlation testing procedures are not available. In order to establish these results we also give a new central limit theorem for linear-quadratic forms.