Multiple outlier detection tests for parametric models

TL;DR

This paper introduces a new multiple outlier detection method for parametric models that outperforms existing techniques in identifying outliers, supported by extensive simulations and an R package implementation.

Contribution

The paper presents a novel outlier detection method based on asymptotic properties of extreme z-scores, applicable to various parametric models, with superior detection power.

Findings

The new method outperforms existing methods in masking and swamping scenarios.

Extensive simulations demonstrate higher outlier detection power.

An R package 'outliersTests' is provided for practical use.

Abstract

We propose a simple multiple outlier identification method for parametric location-scale and shape-scale models when the number of possible outliers is not specified. The method is based on a result giving asymptotic properties of extreme z-scores. Robust estimators of model parameters are used defining z-scores. An extensive simulation study was done for comparing of the proposed method with existing methods. For the normal family, the method is compared with the well known Davies-Gather, Rosner's, Hawking's and Bolshev's multiple outlier identification methods. The choice of an upper limit for the number of possible outliers in case of Rosner's test application is discussed. For other families, the proposed method is compared with a method generalizing Gather-Davies method. In most situations, the new method has the highest outlier identification power in terms of masking and swamping values. We also created R package outliersTests for proposed test.