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Asymptotic properties of a rank estimate in heteroscedastic linear regression
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
(English)Manuscript (Other academic)
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-97605OAI: oai:DiVA.org:uu-97605DiVA: diva2:172614
Available from: 2008-10-10 Created: 2008-10-10 Last updated: 2012-07-26Bibliographically approved
In thesis
1. Rank Estimation in Elliptical Models: Estimation of Structured Rank Covariance Matrices and Asymptotics for Heteroscedastic Linear Regression
Open this publication in new window or tab >>Rank Estimation in Elliptical Models: Estimation of Structured Rank Covariance Matrices and Asymptotics for Heteroscedastic Linear Regression
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with univariate and multivariate rank methods in making statistical inference. It is assumed that the underlying distributions belong to the class of elliptical distributions. The class of elliptical distributions is an extension of the normal distribution and includes distributions with both lighter and heavier tails than the normal distribution.

In the first part of the thesis the rank covariance matrices defined via the Oja median are considered. The Oja rank covariance matrix has two important properties: it is affine equivariant and it is proportional to the inverse of the regular covariance matrix. We employ these two properties to study the problem of estimating the rank covariance matrices when they have a certain structure.

The second part, which is the main part of the thesis, is devoted to rank estimation in linear regression models with symmetric heteroscedastic errors. We are interested in asymptotic properties of rank estimates. Asymptotic uniform linearity of a linear rank statistic in the case of heteroscedastic variables is proved. The asymptotic uniform linearity property enables to study asymptotic behaviour of rank regression estimates and rank tests. Existing results are generalized and it is shown that the Jaeckel estimate is consistent and asymptotically normally distributed also for heteroscedastic symmetric errors.

Place, publisher, year, edition, pages
Uppsala: Universitetsbiblioteket, 2008. 42 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 58
Keyword
elliptical distributions, multivariate ranks, rank covariance matrix, linear rank regression, heteroscedastic errors, linear rank statistics
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-9305 (URN)978-91-506-2026-9 (ISBN)
Public defence
2008-11-03, Polhemsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 10:15
Opponent
Supervisors
Available from: 2008-10-10 Created: 2008-10-10 Last updated: 2012-07-26Bibliographically approved

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