Empirical Influence Functions of Hodges-Lehmann Weighted Estimates Applied in Deformation Analysis

The paper concerns the empirical influence functions of the Hodges-Lehmann weighted estimates (HLWE) of the shift. These estimates are one of the basic R-estimates which may be applied in deformation analysis. The objective of the paper is to examine how occurrence of different number of gross errors in observation sets impact on the empirical influence functions of the Hodges-Lehmann weighted estimates, especially of a new variant which is more reliable that the traditional one. We carry out numerical tests for two cases of HLWEs in comparison to the least square estimates. The results show that the empirical influence functions of the Hodges-Lehmann weighted estimates are bounded functions. These functions are not usually smooth, since they have a few peaks. The empirical influence functions of both cases of HLWEs allow us to find such number of gross errors in observation sets which influence the R-estimate too strongly.