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Activity Number:
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418
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #301438 |
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Title:
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Multivariate Generalized Spatial Signed-Rank Methods
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Author(s):
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Robert J. Serfling*+ and Jyrki Mottonen and Hannu Oja
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Companies:
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The University of Texas, Dallas and University of Oulu and University of Jyvaskyla
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Address:
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1921 Sparrows Point, Plano, TX, 75023,
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Keywords:
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multivariate ; signed-rank tests ; location problem ; relative efficiency ; robustness
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Abstract:
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For the one-sample location problem with data from centrally symmetric distributions, a family of generalized multivariate signed-rank tests are developed and shown to provide a spectrum of favorable trade-offs between efficiency at the normal and protection against heavier-tailed models. The family generalizes the well-known spatial sign and signed-rank tests studied by Mottonen and Oja (1995) and Mottonen, Oja and Tienari (1997). Limiting distributions of test statistics are obtained as well as asymptotic relative efficiencies with respect to the Hotelling's Tand mean tests for data from multivariate normal, t- and contaminated normal distributions. Also treated are related generalized Hodges-Lehmann location estimators. For maximization of efficiency subject to a required level of robustness, the generalized signed-rank methods are found to compare very favorably with competitors. These tests (estimates) are only rotation invariant (equivariant), but construction of affine invariant (equivariant) versions using the transformation-retransformation technique is discussed.
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