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

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.