讲述问题：Fast computing Tukey depth regions of dimensions of p > 2
择要：Given data in R^p, a Tukey tau-trimmed region is the set of all points that have at least Tukey depth tau w.r.t. the data. As they are visual, affine equivariant and robust, Tukey regions are useful tools in nonparametric multivariate analysis. While these regions are easily defined and interpreted, their practical use in applications has been impeded so far by the lack of efficient computational procedures in dimension p > 2. We construct two novel algorithms to compute a Tukey tau-trimmed region, a naive one and a more sophisticated one that is much faster than known algorithms. Further, a strict bound on the number of facets of a Tukey region is derived. In a large simulation study the novel fast algorithm is compared with the naive one, which is slower and by construction exact, yielding in every case the same correct results. Finally, the approach is extended to an algorithm that calculates the innermost Tukey region and its barycenter, the Tukey median. Supplementary material is available online.
现已在中国迷信数学英文版、数学学报中英文版、Journal of Econometrics
(学界公认的计量经济学顶尖期刊，是教诲部承认的12本经济学国际顶级期刊之一)、Journal of Statistical Software(top期刊，2017/2018影响因子22.737)、Journal of Computational and Graphical Statistics、Statistics and Computing等海内外刊物上揭晓任命相干学术论文30篇。刘传授先后掌管国度天然迷信基金区域项目、青年项目、面上项目各1项，掌管中国博士基金一等赞助、稀奇赞助各1项，掌管江西省天然基金青年严重、江西省卓越青年基金各项目1项。同时是Journal of American Statistical Association（JASA）等多个国际期刊的审稿人。