A goodness-of-fit test using Moran's statistic with estimated parameters

Abstract

Moran's log spacings statistic for testing goodness of fit is shown to have the same asymptotic distribution when parameters must be estimated from the sample as it does when parameters are known, provided the estimation is done efficiently. For small samples, a chi-squared approximation is given and shown to be accurate when estimation is carried out by minimizing Mdran's statistic itself regarded as a function of the unknown par ameters. A numerical example is given to show the usefulness of Moran's statistic.