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

Bulut H.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, cilt.49, sa.24, ss.5897-5907, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 24
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1080/03610926.2020.1719420
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.5897-5907
  • Anahtar Kelimeler: Mahalanobis distances, robust distances, minimum regularized covariance estimators, minimum diagonal product estimators, high dimensional data, OUTLIER DETECTION
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.