Robustness of Strategy for Testing Levelling Mark Stability Based on Rank Tests

Abstract

The paper's objective is to examine strategy for monitoring the stability of levelling reference marks, which was proposed in [5], for robustness against gross errors. The strategy in question is based on the application of three robust estimators: R-estimate of vertical displacement (based on rank tests) and two robust estimates of the standard deviation. (Because of the estimates' properties the application of the method is for the moment limited to one dimension networks.) The present paper shows that robustness of the estimates does not result in robustness of the strategy itself. This stems from the origin of outliers. There are two sources of outliers when the stability of reference mark is tested: gross errors and unstable points. Each unstable point generates outliers. If there are too many outlying observations of this type then the strategy cannot be robust against any gross error. The present paper indicates that the robustness of the strategy is strongly dependent on the number of unstable points. Thus, the method cannot be generally regarded as robust against gross errors. However, it is advisable to know when the strategy can withstand a single gross error (or multiple gross errors) and to understand how gross errors may influence the estimation results. The theoretical properties of the estimates and of the strategy are illustrated with two numerical examples.

Keywords:

• DISPLACEMENT
• LEVELLING NETWORK
• ROBUSTNESS
• R-ESTIMATION