Abstract
Tukey's depth offers a powerful tool for nonparametric inference and estimation, but also encounters serious computational and methodological difficulties in modern statistical data analysis. This paper studies how to generalize and compute Tukey-type depths in multi-dimensions. A general framework of influence-driven polished subspace depth, which emphasizes the importance of the underlying influence space and discrepancy measure, is introduced. The new matrix formulation enables us to utilize state-of-the-art optimization techniques to develop scalable algorithms with implementation ease and guaranteed fast convergence. In particular, half-space depth as well as regression depth can now be computed much faster than previously possible, with the support from extensive experiments. A companion paper is also offered to the reader in the same issue of this journal.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Data Science, Statistics, and Visualisation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
