Leptokurtosis of Error Distribution and its Influence on Estimation Accuracy. The Case of Three Estimates Applied in Adjustment of Geodetic Measurements

The paper concerns leptokurtosis of error distribution, which is sometimes present in the case of geodetic or astrometric measurements. We are interested how such a property influence accuracy of three chosen estimates (the least squares estimates, R-estimates and Mp estimates). The choice was due to their practical application in the adjustment of geodetic observations. The analysis is based on Monte Carlo simulations, which were carried out by assuming the normal distribution or Johnson's distributions. In the ladder case we assume different values of excess kurtosis. The results show that leptokurtosis of error distribution might indeed influence estimation accuracy. The accuracy of LSEs does not depend on the excess kurtosis, while the accuracy of HLEs does. The obtained results show that we should consider application of different kinds of estimates when the error distribution is suspected to be leptokurtic and we require estimates with the highest possible accuracy.