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Bounds for the Breakdown Point of the Simplicial Median

โœ Scribed by Z.Q. Chen


Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
394 KB
Volume
55
Category
Article
ISSN
0047-259X

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โœฆ Synopsis


Upper and lower bounds are given for the breakdown point of Liu's empirical simplicial median. This median has a strictly positive breakdown point but is a less robust location estimator than the median based on Tukey's data depth (D. Donoho and M. Gasko, Ann. Statist. 20 (1992), 1803-1827). 1995 Academic Press. Inc.


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It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It