Doubtful Outliers with Robust Regression of an M-estimator In Cluster Analysis

Abstract

Doubtful outlier between clusters may show some meaningful data. In some cases for example it may explain the potential or the unique pattern within the data. However, there is still no further analysis to show how this data (doubtful) connected to one another. In the simulation, we use different threshold values to detect how many doubtful outliers exist between clusters. For these cases we will use 1%, 5%, 10%, 15% and 20% of threshold values. For real data, we fit a linear model using an M estimator with the existences of doubtful data with 10% threshold value. The objective is to determine if doubtful data affect the parameter of M estimator. By comparing using linear model with the deletion of outliers we can conclude that doubtful outlier affect the parameter of M estimator make it less robust towards doubtful outliers in the present of 10% of threshold value. Keywords :Doubtful outlier, Cluster Analysis, Robust Regression, M estimator. 2010 Mathematics Subject Classification: 46N60, 92B99.