Multidimensional trimming based on projection depth
基于投影深度的多维截尾均值AI 解读 ↓
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基于投影深度的多维截尾均值
- 研究问题
- 如何把一维截尾均值的稳健性与效率推广到多维位置估计，并同时评估局部污染敏感性、整体抗污染能力和渐近性质？
- 方法与思路
- 作者利用投影深度生成的区域构造多维截尾均值，以影响函数和有限样本崩溃点分析稳健性，并研究区域方向半径。
- 材料陈述的贡献
- 摘要称获得强一致性、渐近表示和极限分布，并在所考察的正态、对称及污染模型下呈现较高效率和稳健性。
- 阅读关注点
- 应核对投影深度与截尾比例的定义、污染模型、效率比较对象，以及影响函数、崩溃点和渐近结果各自的条件。
- 阅读边界
- 索引摘要未注明稿件版本；效率优势仅是摘要对所考察模型的陈述，具体数值、条件及高维适用性均未说明。
原文摘要
As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed models. This paper introduces multidimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point. The influence function captures the local robustness whereas the breakdown point measures the global robustness of estimators. It is found that the projection depth trimmed means are highly robust locally as well as globally. Asymptotics of the depth trimmed means are investigated via those of the directional radius of the depth induced regions. The strong consistency, asymptotic representation and limiting distribution of the depth trimmed means are obtained. Relative to the mean and other leading competitors, the depth trimmed means are highly efficient at normal or symmetric models and overwhelmingly more efficient when these models are contaminated. Simulation studies confirm the validity of the asymptotic efficiency results at finite samples.