Identifying Multiple Outliers in Linear Functional Relationship Model using a Robust Clustering Method

Outliers are some observation points outside the usual pattern of the other observations. It is essential to detect outliers as anomalous observations can affect the inference made in the analysis. In this study, we propose an efficient clustering procedure to identify multiple outliers in the linear functional relationship model using the single linkage algorithm with the Euclidean distance as the similarity measure. A new robust cut-off point using the median and median absolute deviation for the tree heights to classify the potential outliers are proposed in this study. Experimental results from the simulation study suggest our proposed method is able to identify the presence of multiple outliers with very small probability of swamping and masking. Application in real data also shows that the proposed clustering method for this linear functional relationship model successfully detects the outliers, thus suggesting the method's practicality in real-world problems.