New Approaches for Outlier Detection: The Least Trimmed Squares Adjustment

Abstract

Classical outlier tests based on the least-squares (LS) have significant disadvantages in some situations. The adjustment computation and classical outlier tests deteriorate when observations include outliers. The robust techniques that are not sensitive to outliers have been developed to detect the outliers. Several methods use robust techniques such as M-estimators, L1- norm, the least trimmed squares etc. The least trimmed squares (LTS) among them have a high-breakdown point. After the theoretical explanation, the adjustment computation has been carried out in this study based on the least squares (LS) and the least trimmed squares (LTS). A certain polynomial with arbitrary values has been used for applications. In this way, the performances of these techniques have been investigated.