Work

On the use of OWA functions for robustifying the Lilliefors test of goodness-of-fit to a location-scale family

Year: 2026

Type: article

Abstract: The Lilliefors normality test is a classical extension of the Kolmogorov–Smirnov goodness-of-fit test tailored to assessing normality. A recent modification improves its robustness to outliers by introducing a subsetting function. In this paper, we propose an alternative approach that replaces subsetting functions with Ordered Weighted Averaging (OWA) functions and further generalizes the test to any location-scale family, not only the normal distribution. We conduct extensive experiments on the power of the resulting test for three representative location-scale families—normal, uniform and shifted-exponential—using different weight vectors to define the OWA functions. The results indicate that the best trade-off between robustness and statistical power is achieved by a well-known special class of OWA functions: the order statistics.

Source: Fuzzy Sets and Systems

DOI: 10.1016/j.fss.2026.109893

Authors: Marina Iturrate-Bobes, Raúl Pérez-Fernández, Bernard De Baets

Institutions: Universidad de Oviedo, Ghent University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,550

Funder: Ministerio de Ciencia, Innovación y Universidades