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On the least absolute deviations method for ridge estimation of SURE models
Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.ORCID iD: 0000-0003-2733-4441
Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
2014 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Other academic) Epub ahead of print
Abstract [en]

In this paper we examine the application of the Least Absolute Deviations (LAD) method for ridge-type parameter estimation of Seemingly Unrelated Regression Equations (SURE) models. The methodology is aimed to deal with the SURE models with non-Gaussian error terms and highly collinear predictors in each equation. Some biasing parameters used in the literature are taken and the efficiency of both Least Squares (LS) ridge estimation and the LAD ridge estimation of the SURE models, through the Mean Squared Error (MSE) of parameter estimators, is evaluated.

Place, publisher, year, edition, pages
2014.
Keywords [en]
SURE Models, LAD Estimation, Ridge Regression, Efficiency, Robustness
National Category
Economics and Business
Identifiers
URN: urn:nbn:se:hj:diva-19682DOI: 10.1080/03610926.2012.755203OAI: oai:DiVA.org:hj-19682DiVA, id: diva2:562419
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2019-01-07
In thesis
1. On Median and Ridge Estimation of SURE Models
Open this publication in new window or tab >>On Median and Ridge Estimation of SURE Models
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This doctoral dissertation is a progressive generalization of some of the robust estimation methods in order to make those methods applicable to the estimation of the Seemingly Unrelated Regression Equations (SURE) models. The robust methods are each of the Least Absolute Deviations (LAD) estimation method, also known as the median regression, and the ridge estimation method. The first part of the dissertation consists of a brief explanation of the LAD and the ridge methods. The contribution of this investigation to the statistical methodology is focused on in the second part of the dissertation, which consists of 5 articles.

The first article is a generalization of the median regression to the estimation of the SURE models. The proposed methodology is compared with each of the Generalized Least Squares (GLS) method and the median regression of individual regression equations.

The second article generalizes the median regression on the conventional multivariate regression analysis, i.e., the SURE models with the same design matrices of the equations. The results are compared with the median regression of individual regression equations and the conventionally used OLS estimation method for such models (which is equivalent to the GLS estimation, as well).

In the third article, the author develops ridge estimation for the median regression. Some properties and the asymptotic distribution of the estimator presented are investigated, as well. An empirical example is used to assess the performance of the new methodology.

In the fourth article, the properties of some biasing parameters used in the literature for ridge regression are investigated when they are used for the new methodology proposed in the third article.

In the last article, the methodologies of the four preceding articles are assembled in a more generalized methodology to develop the ridge-type estimation of the LAD method for the SURE models. This article has also provided an opportunity to investigate the behavior of some biasing parameters for the SURE models, which were previously used by some researchers in a non-SURE context.

Place, publisher, year, edition, pages
Jönköping: Jönköping International Business School, 2012. p. 159
Series
JIBS Dissertation Series, ISSN 1403-0470 ; 083
National Category
Economics and Business
Identifiers
urn:nbn:se:hj:diva-19681 (URN)978-91-86345-36-5 (ISBN)
Public defence
2012-11-16, B1014 at JIBS, Högskoleområdet Gjuterigatan 5, Jönköping, 10:00
Opponent
Supervisors
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2018-06-07Bibliographically approved

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Zeebari, ZanginShukur, Ghazi

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