Abstract
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.
Highlights
In geodesy, geophysics and many other scientific branches we are confronted with observations affected by observation errors
The paper is organized as follows: After introducing well and less well known models of observation errors we briefly review the Anderson-Darling (AD) test in its special form as a test for normality. Opposed to this we propose the strategy of observation error model selection by Akaike information criterion (AIC)
It has been investigated that the results presented here do not change significantly when the computations are repeated with different pseudo random number (PRN), such that M = 10000 is sufficiently large to support the conclusions made below
Summary
Geophysics and many other scientific branches we are confronted with observations affected by observation errors. The normal distribution, mostly credited to C.F. Gauss, is the best known model of geodetic and geophysical observation errors. The paper is organized as follows: After introducing well and less well known models of observation errors we briefly review the Anderson-Darling (AD) test in its special form as a test for normality. Opposed to this we propose the strategy of observation error model selection by AIC. The Monte Carlo method is used to investigate and compare both strategies applied to the model of a straight line fit
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