RDELA—a Delaunay-triangulation-based, location and covariance estimator with high breakdown point

被引：0
作者：
Steffen Liebscher
Thomas Kirschstein
Claudia Becker
机构：
[1] Martin-Luther-University,
来源：
Statistics and Computing | 2013年 / 23卷
关键词：
Breakdown point; Delaunay triangulation; Minimum covariance determinant; Robust estimation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We propose an approach that utilizes the Delaunay triangulation to identify a robust/outlier-free subsample. Given that the data structure of the non-outlying points is convex (e.g. of elliptical shape), this subsample can then be used to give a robust estimation of location and scatter (by applying the classical mean and covariance). The estimators derived from our approach are shown to have a high breakdown point. In addition, we provide a diagnostic plot to expand the initial subset in a data-driven way, further increasing the estimators’ efficiency.
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页码：677 / 688
页数：11
相关论文
共 53 条
[11]  
Cignoni P.(1934)Sur la sphere vide Izv. Akad. Nauk SSSR, Ser. VII, Otd. Mat. Est. Nauk 7 793-124
[12]  
Montani C.(1972)Robust estimates, residuals, and outlier detection with multiresponse data Biometrics 28 81-14
[13]  
Scopigno R.(1982)Euclidean distance geometry Math. Sci. 7 1-470
[14]  
Croux C.(1974)Algorithm as 78: the mediancentre J. R. Stat. Soc., Ser. C, Appl. Stat. 23 466-119
[15]  
Haesbroeck G.(2008)High-breakdown robust multivariate methods Stat. Sci. 23 92-336
[16]  
Davies P.(2012)The flood algorithm—a multivariate, self-organizing-map-based, robust location and covariance estimator Stat. Comput. 22 325-1665
[17]  
Davies P.(1999)Asymptotics of reweighted estimators of multivariate location and scatter Ann. Stat. 27 1638-248
[18]  
Davies P.(1991)Breakdown points of affine equivariant estimators of multivariate location and covariance matrices Ann. Stat. 19 229-317
[19]  
Gather U.(2002)Robust estimates of location and dispersion for high-dimensional datasets Technometrics 44 307-184
[20]  
Davies P.(1970)The maximum numbers of faces of a convex polytope Mathematika 17 179-123
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