Data depth approach in fitting linear regression models

Abstract

The data depth approach plays a vital role in regression and multivariate analysis. It is a recently emerging research topic in statistics. Regression techniques are mainly used for analysing and modelling multifactor data, it spans a large collection of applicative scenarios in many fields such as the developing discipline of data science which includes machine learning. This paper explores the idea of regression depth. The study is carried out the computational aspects of regression depth for a given dataset under classical and robust methods, like Least Squares (LS), Least Median Squares (LMS) and S-Estimator (S) along with Regression Depth Median (RDM) approach. Further, it is demonstrated the fitted models under various methods and their efficiencies have been studied under the regression depth approach. It is observed that regression depth under robust procedures outperforms the conventional regression procedure under with and without extreme observations in the data. It is concluded that researchers can apply the data depth procedure wherever the model fitting is required when the data contains extremes.