Observation error model selection by information criteria vs. normality testing

To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test