What is the relation between smearing effect of least squares estimation and its influence function?

Abstract

In some cases, tests for outliers and robust methods based on the Least Square Estimation (LSE) fail to detect and isolate outliers. LSE 'smears the effect' of an outlier on all estimates of the residuals, the unknowns, and the a posteriori variance of unit weight. Therefore as bias goes to infinity, the Influence Function (IF) also goes to infinity. This study aims to investigate the effect of an outlier on the unknown parameters, etc., compared to the IF concept. Moreover, how the ratio of the resulting outlier effect is related to the redundancy of the geodetic network has been shown through the concepts of Sensitivity Curve (SC) and smearing effect by Monte Carlo Simulation. Also, it has proved that the SC of LSE was almost equal to the 'smearing effect' of LSE, which behaves systematically as a function of the partial redundancy that varies from one residual to another in the geodetic network.