Robust Statistical Estimation Methods for Multivariate Data in the Presence of Outliers: Theory and Computational Approaches

ABSTRACT One of the most significant issues that multivariate data has in terms of statistical trustworthiness is the presence of outliers. This is due to the fact that the data points influence the final findings while simultaneously providing erroneous conclusions. approaches that reduce the impact of outliers on statistical estimate and improve the accuracy and reliability of statistical results are the focus of this study analysing approaches. From both a theoretical and a programming point of view, the study addresses the construction of sturdy estimators. M-estimators and S-estimators that make use of resilient covariance matrices throughout their implementation in complicated high-dimensional data structures are subjected to a comprehensive analysis in this journal article. Using studies based on fake datasets and providing examples from real-world situations, the study offers proof that these approaches provide reliable point estimates when dealing with data that contains outliers. This study provides useful information to academic researchers as well as practitioners that work with multi-dimensional data, notably in the disciplines of biology and the environment, as well as the financial sector.