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.

Keywords:

• Influence Function
• Sensitivity Curve
• Least Squares Estimation
• Median
• Outlier Diagnostics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Utkan Mustafa Durdag

Utkan Mustafa Durdag received his PhD from Yildiz Technical University Istanbul, in the field of reliability of deformation analysis models for geodetic networks. Since 2019, he is employed at Artvin Coruh University, where his current research interests involve the statistical analysis of geodetic measurements.

Serif Hekimoglu

Serif Hekimoglu is a retired professor from the Yildiz Technical University. He received his PhD from the Institute of Theoretical Geodesy at the University of Bonn in 1976. His research interests involve robust statistical analysis of outlier detection and deformation analysis in geodetic networks.

Bahattin Erdogan

Bahattin Erdogan has been working in Yildiz Technical University, Faculty of Civil Engineering, Department of Geomatic Engineering, Istanbul, Turkey, since 2005. He obtained his PH.D. degree in 2011 and awarded as associate professorship in geodesy in 2015. He is the editor of Journal of Geodesy and Geoinformation since 2019. His research interests are in the field of statitistical analysis of geodetic measurements, robust statistics and precise GNSS positioning.