AFFINE EQUIVARIANT MULTIVARIATE RANK-BASED AND GENERALIZED RANK REGRESSION

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AuthorSalman, Majeda
metadata.dc.contributor.departmentWestern Michigan University
metadata.dc.date.accessioned2026-09-20T15:52:47Z
Publication date2004
Degree levelDoctoral
AbstractAbstract : Affine equivariant estimates for the regression coefficient matrix of the mul- tivariate linear model are proposed. These estimates are based on a transformation and retransformation technique that uses Tyler's (1987) M-estimator of scatter. The proposed estimates are obtained by retransforming the componentwise rank- based estimate due to Davis and McKean (1993) and a componentwise generalized rank estimate. Asymptotic properties of the estimates are established under some regularity conditions. It is shown that both estimates have a multivariate nor- mal limiting distribution. The influence function of the retransformed generalized rank estimate has a bounded influence in both factor and response spaces. It is shown through a simulation study that the transformed-retransformed R and GR estimates are highly efficient compared to the non-equivariant componentwise R, GR and least absolute deviations estimates. Also, it is shown that the new esti- mates perform better than the least squares estimate when the errors have a heavy tailed distribution. Based on the new estimates quadratic procedures for testing the general hypothesis H0 : HBK = 0 are developed. Examples illustrating the estimation and testing procedures are presented.
metadata.dc.identifier.otherDrupal node 4253
metadata.dc.identifier.otherhttps://digitalrepository.uob.edu.bh/en/dar/affine-equivariant-multivariate-rank-based-and-generalized-rank-regression
metadata.dc.identifier.urihttp://165.227.56.122/handle/123456789/7368
Languageen
Linkhttps://digitalrepository.uob.edu.bh/en/_flysystem/fedora/2025-09/001652_affine_equivariant_multivariate_rank-based_and_generalized_rank_regression.pdf
SubjectEstimation theory
SubjectLinear models--Statistics
TitleAFFINE EQUIVARIANT MULTIVARIATE RANK-BASED AND GENERALIZED RANK REGRESSION
TypeDoctoral Dissertation

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