Hodges-Lehmann estimates in deformation analyses

Abstract

This paper presents new variants of the Hodges-Lehmann estimates, which belong to the class of R-estimates. The new approach to this method arises from the need of taking into account differences in accuracy of geodetic measurements, which is not possible while applying traditional R -estimates. The theoretical assumptions of the conventional Hodges-Lehmann estimates are supplemented with the information about the accuracy of observations and two new variants of the estimates in question are derived by applying the principles proposed by Hodges and Lehmann, hence they are called the Hodges-Lehmann weighted estimate. The main properties of the new estimates follow from such approach, and from the practical point of view, the most important seems to be their robustness against outliers. Since the first estimate proposed is a natural estimator of the shift between two samples, it can be applied in deformation analysis to estimate point displacements. The paper presents two numerical examples that show the properties as well as possible applications of the new estimates. © 2013 The Author(s).