# Fast implementation of the Tukey depth

Xiaohui Liu ()
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Xiaohui Liu: Jiangxi University of Finance and Economics

Computational Statistics, 2017, vol. 32, issue 4, 1395-1410

Abstract: Abstract Tukey depth function is one of the most famous multivariate tools serving robust purposes. It is also very well known for its computability problems in dimensions $$p \ge 3$$ p ≥ 3 . In this paper, we address this computing issue by presenting two combinatorial algorithms. The first is naive and calculates the Tukey depth of a single point with complexity $$O\left( n^{p-1}\log (n)\right)$$ O n p - 1 log ( n ) , while the second further utilizes the quasiconcave of the Tukey depth function and hence is more efficient than the first. Both require very minimal memory and run much faster than the existing ones. All experiments indicate that they compute the exact Tukey depth.

Keywords: Tukey depth; Quasiconcave; Combinatorial property; Fast computation (search for similar items in EconPapers)
Date: 2017
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