Empirical analyses of robustness of the square Msplit estimation

The paper presents M-split estimation as an alternative to methods in the class of robust M-estimation. The analysis conducted showed that M-split estimation is highly efficient in the identification of observations encumbered by gross errors, especially those of small or moderate values. The classical methods of robust estimation provide then unsatisfactory results. M-split estimation also shows high robustness to single gross errors of large values. The presented analysis of M-split estimators' robustness is of a chiefly empirical nature and is based on the example of a simulated levelling network and a real angular-linear network. Using the Monte Carlo method, mean success rates for outlier identification were determined and the courses of empirical influence functions were specified. The outcomes of the analysis were compared with the relevant values achieved via selected methods of robust M-estimation.

Automated summary

The paper introduces M-split estimation as an alternative to robust M-estimation methods and found it to be highly efficient in identifying observations affected by gross errors, while also showing robustness to single gross errors of large values. The analysis is primarily empirical and based on simulated and real networks, with comparison to selected robust M-estimation methods.