Empirical influence functions and their non-standard applications

Abstract

The main objective of the empirical influence function (EIF) is to describe how estimates behave when an observation set is affected by gross errors. Unlike the influence function, which represents the estimation method’s general properties, EIF can provide valuable information about applying different methods to a particular network. The chosen example allows us to compare different robust methods. The paper focuses on non-standard applications of EIF, for example, in assuming steering parameter of robust methods (usually related to the assumed interval for acceptable observation errors). The paper shows that commonly used values do not always work well, and EIFs might help choose appropriate values, guaranteeing the estimation process’s robustness. The most important new application of EIFs concerns the detection and assessment of a single gross error. The blinded experiments proved that such an approach is correct and can be an alternative to classic statistical tests for outlier detection.

Robust procedures in processing measurements in geodesy and surveying: a review

“…The presented procedures and others used in statistics are successful if only one outlier occurs. That problem was addressed by referring to the geodetic issues in many papers [7,37,[39][40][41]. The authors conclude that in the case of multiple outliers, data snooping methods or other procedures for outlying detection often fail, which stems from different adverse effects of outlier occurrence, including maskingwhen one outlier 'masks' occurrence of the other, swampingwhen an outlier 'makes' a regular observation suspicious, or smearing-when outliers influence all (or most of) estimation results badly (e.g.…”

“…The authors conclude that in the case of multiple outliers, data snooping methods or other procedures for outlying detection often fail, which stems from different adverse effects of outlier occurrence, including maskingwhen one outlier 'masks' occurrence of the other, swampingwhen an outlier 'makes' a regular observation suspicious, or smearing-when outliers influence all (or most of) estimation results badly (e.g. [41][42][43][44][45]). Therefore, some authors proposed modifying or improving conventional methods to detect multiple outliers more effectively.…”

“…The presented procedures are not the only solutions to the outlying observation problem in geodetic data processing. One can find the other based on or using, for example, Bayesian estimation [44], empirical influence function analysis [41], Monte Carlo simulations [4,47,48], changing stochastic observation model [49], etc. No doubt that their efficiency or effectiveness, hence also a proper choice, depends on a particular geodetic problem or network, the type of observations involved, and also the type, number, location, and magnitude of outliers.…”