Multidimensional trimming based on projection depth
By Yijun Zuo. 2006
65 citations recorded by the source corpus.
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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/4ba2b8d4300c29d9540304d753dcd344000ad8aa
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In Statistics and Probability
- Anirvan Chakraborty
- Probal Chaudhuri
- Pavlo Mozharovskyi
- Karl Mosler
- Francesca Molinari
- Arie Beresteanu
- Anil Kumar Ghosh
Citations in the corpus
- On data depth in infinite dimensional spaces (2014, methodology): “in developing several statistical procedures. Depth-weighted L-type location estimators like trimmed means have been considered in Donoho and Gasko (1992), Fraiman and Muniz (2001), Mosler (2002) and Zuo (2006). Depth functions have also been used to construct statistical classifiers (see, e.g., Jo¨r”
- Choosing Among Notions of Multivariate Depth Statistics (2020, background): “Another indicator of robustness of a depth is the influence function of its median; it is investigated in Romanazzi (2001) for halfspace depth, in Niinimaa and Oja (1995) for L2-, spatial, and Oja depth, in Zuo (2004) for Lp depth, and in Zuo (2006) for projection depth.”