Where does the Heaviness Start?

Accepted - July 2024

Abstract

Datasets with a heavy-tailed histogram tend to have a large number of outliers, which provide important information. As a result, the bulk part and tail part of the dataset with this feature have different characteristics. Then, the choice of a threshold that separates these two parts is important. We propose a novel approach based on the Empirical Likelihood method to estimate this threshold. Because the transition between the bulk and tail parts cannot be fully disjointed in many cases, we allow the threshold to be a random variable instead of a fixed number. In addition, the threshold is relative to a benchmark since heaviness is a relative concept.