JSM 2004 - Toronto

Abstract #302269

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Activity Number: 98
Type: Invited
Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
Sponsor: JASA, Theory and Methods
Abstract - #302269
Title: Location-scale Depth
Author(s): Ivan Mizera*+ and Christine H. Mueller
Companies: University of Alberta and Carl Von Ossietzky University of Oldenburg
Address: Dept. of Math & Statistical Sciences, Edmonton, AB, T6G 2G1, Canada
Keywords: depth contours ; exploratory data analysis ; location-scale model ; median ; Mobius equivariance ; robust estimation
Abstract:

The paper introduces a half-space depth in the location-scale model, along the lines of the general theory given by Mizera on the basis of the idea by Rousseeuw and Hubert, complemented by a new likelihood-based principle for designing criterial functions. The most tractable version of the proposed depth, the Student depth, turns out to be nothing but the bivariate half-space depth interpreted in the Poincare plane model of the Lobachevski geometry. This fact implies many fortuitous theoretical and computational properties, in particular, equivariance with respect to the Mobius group and favorable time complexities of algorithms. It also opens a way to introduce some other depth notions in the location-scale context, for instance, location-scale simplicial depth. A maximum depth estimator of location and scale--the Student median--is introduced. Possible applications of the proposed concepts are investigated on data examples.

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