Computing Robust Measure of Location on Multivariate Statistical Data Using Euclidean Depth Procedures

Abstract

Objectives: To suggest reliable location parameters (central value) in multivariate datasets using data depth procedures in order to reduce the presence of outliers. Methods: Applying depth techniques in both outlier-free and outliercontaining scenarios, the data sets starsCYG and delivery time data are utilized to determine the measure of location. Various classical and robust data depth procedures are used to find the location parameters, namely Mahalanobis depth, Tukey's half space depth, Projection depth, Zonoid depth, Spatial depth, and L2 Depth (Euclidean Depth). Distance-Distance plot is used for identifying the outliers. Further, it has been researched how well the data depth processes work by computing the parameters under actual and simulation environments, with and without outliers by considering different levels of contaminations (0%, 1%, 2%, 3%, 5%, 10%, 20%, 30%, 40%). Findings: From the two data sets studied, Halfspace depth and Euclidean (using MCD estimator) give the same location parameters if the anomalies are present. These two procedures work equally well and more effectively than the others. The robust depth procedures work well if the outliers are present in the datasets and from the simulation study it can handle a certain level of contamination present in the data set. Novelty: Any dataset that contains outliers makes analysis results risky. Robust statistical techniques can tolerate some getting contaminated. According to the study, even if the data contains outliers, the Depth processes employing robust estimators can withstand a certain amount of contamination and still produce accurate findings.