Robust Multivariate Location Estimation in the Existence of Casewise and Cellwise Outliers

Abstract

Multivariate outliers can exist in two forms, casewise and cellwise. Data collection typically contains unknown proportion and types of outliers which can jeopardize the location estimation and affect research findings. In cases where the two coexist in the same data set, traditional distance-based trimmed mean and coordinate-wise trimmed mean are unable to perform well in estimating location measurement. Distance-based trimmed mean suffers from leftover cellwise outliers after the trimming whereas coordinate-wise trimmed mean is affected by extra casewise outliers. Thus, this paper proposes new robust multivariate location estimation known as α-distance-based trimmed median (<img src=image/13491675_01.gif>) to deal with both types of outliers simultaneously in a data set. Simulated data were used to illustrate the feasibility of the new procedure by comparing with the classical mean, classical median and α-distance-based trimmed mean. Undeniably, the classical mean performed the best when dealing with clean data, but contrarily on contaminated data. Meanwhile, classical median outperformed distance-based trimmed mean when dealing with both casewise and cellwise outliers, but still affected by the combined outliers' effect. Based on the simulation results, the proposed <img src=image/13491675_01.gif> yields better location estimation on contaminated data compared to the other three estimators considered in this paper. Thus, the proposed <img src=image/13491675_01.gif> can mitigate the issues of outliers and provide a better location estimation.