Precision Index in the Multivariate Context

Abstract

General multivariate quantiles are employed to extend the classic univariate process precision index to the multivariate context under very mild conditions. Using halfspace depth regions for this purpose is especially recommended because it leads to both computational simplicity and natural generalizations to the tool-wear setup thanks to some recent advances in multiple-output and projectional quantile regression. A few examples are included to illustrate how the methodology might work in practice.

Keywords:

• Data depth
• Multivariate quantile
• Precision index
• Process capability index
• Regression quantile

Mathematics Subject Classification:

• Primary 62P30
• Secondary 62G05, 62G15

Acknowledgments

The author would like to thank Jiří Michálek for careful reading of the manuscript and Davy Paindaveine, Marc Hallin, Claude Adan, Nancy de Munck, and Romy Genin for all the good they did for him (and for all the good he could learn from them) during his stay at Université Libre de Bruxelles.