The Distribution of Robust Distances
Mahalanobis squared distance, Minimum covariance determinant, Outlier detection, Robust estimation
Mahalanobis-type distances in which the shape matrix is derived from a consistent, high-breakdown robust multivariate location and scale estimator have an asymptotic chi-squared distribution as is the case with those derived from the ordinary covariance matrix. For example, Rousseeuw's minimum covariance determinant (MCD) is a robust estimator with a high breakdown. However, even in quite large samples, the chi-squared approximation to the distances of the sample data from the MCD center with respect to the MCD shape is poor. We provide an improved F approximation that gives accurate outlier rejection points for various sample sizes.
© 2005 Taylor and Francis
Hardin, J., Rocke, D.; The Distribution of Robust Distances; Journal of Computational and Graphical Statistics, 14: 928-946; 2005. doi: 10.1198/106186005X77685