Mahalanobis distance based on minimum regularized covariance determinant estimators for high dimensional data

Abstract

Outlier detection is an extensively studied issue in robust literature. The most popular and traditional approach using to detect outliers is to calculate the Mahalanobis distance. However, conventional Mahalanobis distances may fail to detect outliers because they base on the classical sample mean vector and covariance matrix, which are sensitive to outliers. To solve this problem, the Minimum Covariance Determinant (MCD) estimators are used instead of classical estimators. However, the MCD estimators cannot be calculated in high dimensional data sets, which variable number p is higher than the sample size n. To detect outliers in high dimensional data, we propose Mahalanobis distance based on the Minimum Regularized Covariance Determinants (MRCD) estimators, which can be calculated in high dimensional data sets. We have shown that this distance is successful for outlier detection in high dimensional data sets with the simulation study and real data sets.

Keywords:

• Mahalanobis distances
• robust distances
• minimum regularized covariance estimators
• minimum diagonal product estimators
• high dimensional data