A new non-parametric detector of univariate outliers for distributions with unbounded support

TL;DR

This paper introduces a new non-parametric univariate outlier detector based on a Hill's type statistic, demonstrating strong asymptotic properties and superior accuracy over existing methods through simulations and real-world car price data.

Contribution

It develops a novel outlier detection method for unbounded distributions and analyzes its asymptotic behavior, with validation via simulations and real data application.

Findings

The detector performs well compared to traditional methods.

It has strong asymptotic properties for various distributions.

Effective in real-world used car price data.

Abstract

The purpose of this paper is to construct a new non-parametric detector of univariate outliers and to study its asymptotic properties. This detector is based on a Hill's type statistic. It satisfies a unique asymptotic behavior for a large set of probability distributions with positive unbounded support (for instance: for the absolute value of Gaussian, Gamma, Weibull, Student or regular variations distributions). We have illustrated our results by numerical simulations which show the accuracy of this detector with respect to other usual univariate outlier detectors (Tukey, MAD or Local Outlier Factor detectors). The detection of outliers in a database providing the prices of used cars is also proposed as an application to real-life database.