刘小惠学术报告通知
一、报告题目：Some results on Tukey's halfspace depth regions and median
二、报告人： 刘小惠——江西财经大学数学与统计学院
三、报告时间：2018-6-4下午4:00-5:00
四、报告地点：数学与统计学院会议室90510
五、参加人员：学院相关学科老师及统计学研究生
六、报告人简介：
刘小惠，江西财经大学统计学院副教授，主要研究方向为稳健统计、时间序列分析、统计计算、经验似然，现已在中国科学数学英文版、Journal of Econometrics、Journal of Statistical Software等国内外刊物上发表录用相关学术论文近30篇；主持国家自然科学基金两项，中国博士基金一等资助、特别资助各一项，主持江西省省级青年重大项目一项。
七、报告摘要：
Given data in $\mathbb{R}^{p}$, a Tukey $\kappa$-trimmed region, shortly Tukey $\kappa$-region or just Tukey region, is the set of all points that have at least Tukey depth $\kappa$ 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 application is impeded by the lack of efficient computational procedures in dimension $p > 2$. In first part of this talk, I will present a strict bound on the number of facets of a Tukey region and construct a new efficient algorithm to compute the region, which runs much faster than existing ones.
As the average of all point in the innermost region, Tukey's halfspace median ($\HM$), servicing as the multivariate counterpart of the univariate median, has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness property (the most outstanding property) of the univariate median. One of prevalent quantitative assessments of robustness is finite sample breakdown point (FSBP). Indeed, the FSBP of many multivariate medians have been identified, except for the most prevailing one---the Tukey's halfspace median. In the second part of this talk, I'd like to present a precise result on FSBP for Tukey's halfspace median. The result here depicts the complete prospect of the global robustness of $\HM$ in the finite sample practical scenario, revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.
