Similarities Between Location Depth and Regression Depth View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2001

AUTHORS

Mia Hubert , Peter J. Rousseeuw , Stefan Van Aelst

ABSTRACT

ℝ In this paper we first explore the analogies between location depth and regression depth. The location depth of [Tukey (1975)] is a multivariate generalization of rank, and leads to a multivariate median known as the Tukey median or the deepest location. Regression depth was introduced in [Rousseeuw and Hubert (1999b)], and yields the deepest regression which is a new robust regression estimator. Based on the recent literature on depth, we compare several theoretical and computational aspects of depth and of the deepest fits in location and regression. The depth of a fit can also be defined with regard to a population distribution. Here, we derive the depth functions at elliptical distributions. Finally we introduce the centrality of a location fit and a regression fit. Centrality is a new and more quantitative version of depth that leads to affine equivariant estimators of location and regression with 50% breakdown value. More... »

PAGES

159-172

Book

TITLE

Statistics in Genetics and in the Environmental Sciences

ISBN

978-3-0348-9518-7
978-3-0348-8326-9

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-8326-9_11

DOI

http://dx.doi.org/10.1007/978-3-0348-8326-9_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020188471


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