The Distribution of Robust Distances

Authors

Johanna S. Hardin, Pomona CollegeFollow
David M. Rocke, University of California - Davis

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2005

Keywords

Mahalanobis squared distance, Minimum covariance determinant, Outlier detection, Robust estimation

Abstract

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.

Rights Information

© 2005 Taylor and Francis

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1198/106186005X77685

Recommended Citation

Hardin, J., Rocke, D.; The Distribution of Robust Distances; Journal of Computational and Graphical Statistics, 14: 928-946; 2005. doi: 10.1198/106186005X77685