On Generalization and Computation of Tukey's Depth: Part I





Tukeyfication, estimating equations, projected cone depth, polished subspace depth, Procrustes rotation, Nesterov's acceleration, nonparametric inference


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.

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How to Cite

She, Y., Tang, S. ., & Liu, J. (2022). On Generalization and Computation of Tukey’s Depth: Part I. Journal of Data Science, Statistics, and Visualisation, 2(1). https://doi.org/10.52933/jdssv.v2i1.23