Robust Multivariate Outlier Labeling

Abstract

A criterion for robust estimation of location and covariance matrix is considered, and its application in outlier labeling is discussed. This method, unlike the methods based on MVE and MCD, is applicable to large and high-dimension data sets. The method proposed here is also robust and has the same breakdown point as the MVE-and MCD-based methods. Furthermore, the computational complexity of the proposed method is significantly smaller than that of other methods.

Monitoring the Stability of Correlation Structure in Drive Rib Production Process: An MSPC Approach

“…A more general presentation and discussion on vector variance can be found in our recent work (Djauhari 2007) [24]. See also (Herwindiati et al, 2007) [26] for its application in robust estimation of location and scatter.…”

“…This is a reason why, in the present paper, we propose VVSV-based statistic instead of Box's M statistic and Jennrich's statistic. It is also due to this advantage that in (Herwindiati et al, 2007) [26] we use VV to increase the computational efficiency in data concentration step of FMCD algorithm. More precisely, we use minimum vector variance (MVV) as the stopping rule to substitute the minimum covariance determinant (MCD) which, as mentioned above, has high computational complexity.…”

“…The asymptotic distribution of sample VV is investigated using the notations in (Serfling 1980) [29]. Its successful application as the stopping rule in FMCD (fast minimum covariance determinant) algorithm can be seen in (Herwindiati et al, 2007) [26]. It reduces significantly the computational complexity of FMCD in data concentration step.…”

“…As a multivariate dispersion measure, vector variance (VV) is proposed heuristically in our recent work (Herwindiati et al, 2007) [26] and analytically in our other work (Djauhari 2007) [24]. It is derived from the notion of vector covariance presented and used in (Cleroux 1987) [27], and originally introduced by (Escoufier 1973) [28] to measure the linear relationship between two random vectors.…”

An Alternative Hotelling T^2 Control Chart Based on Minimum Vector Variance (MVV)

“…Furthermore, as noted by Fauconnier and Haesbroeck (2009), Fast MCD algorithm may return different results when used repeatedly in the same or in different statistical packages and could be more critical when n/p are small. To overcome the weaknesses of Fast MCD algorithm, Herwindiati (2006) proposed minimum vector variance (MVV) as an alternative measure of multivariate data concentration. Herwindiati et al (2007) revealed that MVV was successfully used as an objective function in Fast MCD algorithm to substitute the MCD criterion.…”