On Exact Computation of Some Statistics Based on Projection Pursuit in a General Regression Context

Abstract

It is shown in detail how recent advances in multiple-output and projectional quantile regression open the door to exact computation of many inferential statistics based on projection pursuit. This is also illustrated on a few examples including new regression generalizations of multivariate skewness, kurtosis, and projection depth.

Keywords:

• Exact computation
• Multivariate quantile
• Projection depth
• Projection pursuit
• Quantile regression
• Regression depth

Mathematics Subject Classification:

• 62H02
• 62J05
• 62F35
• 90C25

Acknowledgments

This research work of Miroslav Šiman was supported by Project 1M06047 of the Ministry of Education, Youth and Sports of the Czech Republic. The author would also like to thank 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 recent stay at Université Libre de Bruxelles.