A Comparison of Various Robust Estimators in Mahalanobis Depth

Surabhi S Nair

Abstract: One of the fundamental ideas in multidimensional data analysis is data depth. The phrase data depth refers to the depth of a specific point within a large multivariate data cloud. The sample points can be ranked from the center outward rather than the usual smallest to biggest rank. This is one method for identifying a good representation across the entire data. The Mahalanobis Depth (MD) approach, which is one of the most used depth methods, is based on the standard mean vector and covariance matrix. If certain presumptions are valid, conventional MD should function quite well; nevertheless, while a few of these assertions are false, traditional MD may not be reliable. Anomalies are very likely to occur in both the sample mean vector and covariance matrix. Due to this, the classic Mahalanobis depth is unable to produce accurate findings when the data contains abnormalities. As a result, this work proposed a set of robust Mahalanobis depths for location estimation namely Robust MD based on M-estimator (RMD - M), MM estimator (RMD - MM), and Minimum Regularized Covariance Determinant estimator (RRMD- Robust Regularized Mahalanobis Depth). All the proposed depth functions work well and give reliable location when the data is not high-dimensional, the variable number p is less than sample size n. But in the high dimensional data set, where variable number p is greater than sample size n, some of the proposed MD cannot be determined. Even with high-dimensional and corrupted data, one of the proposed depth functions RRMD produces credible findings when compared to existing approaches and other proposed depth functions in this study. In comparison to other depth functions that have been suggested, this study demonstrates that RRMD is successful in locating a central point even in high-dimensional data sets with real data study and simulation study up to a specific level of contamination.

Keywords: Mahalanobis depth, Outliers, Robust distance, Robust estimators

How to Cite?: Surabhi S Nair, "A Comparison of Various Robust Estimators in Mahalanobis Depth", Volume 14 Issue 7, July 2025, International Journal of Science and Research (IJSR), Pages: 835-839, https://www.ijsr.net/getabstract.php?paperid=SR25711214912, DOI: https://dx.doi.org/10.21275/SR25711214912