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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.

Empirical influence functions and their non-standard applications