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On Median and Ridge Estimation of SURE Models
Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
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. , 159 p.
Series
JIBS Dissertation Series, ISSN 1403-0470 ; 083
National Category
Economics and Business
Identifiers
URN: urn:nbn:se:hj:diva-19681ISBN: 978-91-86345-36-5 (print)OAI: oai:DiVA.org:hj-19681DiVA: diva2:562429
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: 2012-10-24Bibliographically approved
List of papers
1. On the median regression for SURE models with applications to 3-generation immigrants data in Sweden
Open this publication in new window or tab >>On the median regression for SURE models with applications to 3-generation immigrants data in Sweden
2011 (English)In: Economic Modelling, ISSN 0264-9993, E-ISSN 1873-6122, Vol. 28, no 6, 2566-2578 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we generalize the median regression method to be applicable to system of regression equations, in particular SURE models. Giving the existence of proper system wise medians of the residuals from different equations, we apply the weighted median regression with the weights obtained from the covariance matrix of the equations obtained from ordinary SURE method. The benefit of this model in our case is that the SURE estimators utilise the information present in the cross regression (or equations) error correlation and hence more efficient than other estimation methods like the OLS method. The Seemingly Unrelated Median Regression Equations (SUMRE) models produce results that are more robust than the usual SURE or single equations OLS estimation when the distributions of the dependent variables are not normally distributed or the data are associated with outliers. Moreover, the results are also more efficient than is the cases of single equations median regressions when the residuals from the different equations are correlated. A theorem is derived and indicates that even if there is no statistically significant correlation between the equations, using SUMRE model instead of SURE models will not damage the estimation of parameters.

Keyword
Median regression, SURE models, Robustness, Efficiency
National Category
Economics and Business
Identifiers
urn:nbn:se:hj:diva-19672 (URN)10.1016/j.econmod.2011.07.010 (DOI)
Available from: 2012-10-23 Created: 2012-10-23 Last updated: 2017-12-07Bibliographically approved
2. Median regression for SUR models with the same explanatory variables in each equation
Open this publication in new window or tab >>Median regression for SUR models with the same explanatory variables in each equation
2012 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 39, no 8, 1765-1779 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we introduce an interesting feature of the generalized least absolute deviations method for seemingly unrelated regression equations (SURE) models. Contrary to the collapse of generalized leasts-quares parameter estimations of SURE models to the ordinary least-squares estimations of the individual equations when the same regressors are common between all equations, the estimations of the proposed methodology are not identical to the least absolute deviations estimations of the individual equations. This is important since contrary to the least-squares methods, one can take advantage of efficiency gain due to cross-equation correlations even if the system includes the same regressors in each equation.

National Category
Economics and Business
Identifiers
urn:nbn:se:hj:diva-19675 (URN)10.1080/02664763.2012.682566 (DOI)
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2017-12-07Bibliographically approved
3. Developing ridge estimation method for median regression
Open this publication in new window or tab >>Developing ridge estimation method for median regression
2012 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 39, no 12, 2627-2638 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, the ridge estimation method is generalized to the median regression. Though the least absolute deviation (LAD) estimation method is robust in the presence of non-Gaussian or asymmetric error terms, it can still deteriorate into a severe multicollinearity problem when non-orthogonal explanatory variables are involved. The proposed method increases the efficiency of the LAD estimators by reducing the variance inflation and giving more room for the bias to get a smaller mean squared error of the LAD estimators. This paper includes an application of the new methodology and a simulation study as well.

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-19676 (URN)10.1080/02664763.2012.724663 (DOI)
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2017-12-07Bibliographically approved
4. A Simulation Study on the Least Absolute Deviations Method for Ridge Regression
Open this publication in new window or tab >>A Simulation Study on the Least Absolute Deviations Method for Ridge Regression
2012 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed) Submitted
Abstract [en]

Though the Least Absolute Deviations (LAD) method of estimation is robust, there is still the possibility of having strong multicollinearity of the predictors in a linear regression analysis. The paper consists of the application of the LAD estimation instead of the Ordinary Least Squares (OLS) estimation for the ridge regression and a simulation study to assess the performance of some biasing parameters used in the literature with their new LAD versions. The aim is to deal with the cases when the predictors are highly collinear  and the error terms are asymmetric or heavy-tailed, by giving more room to the bias in order to reduce the Mean Squared Error (MSE) of the LAD estimators.

Place, publisher, year, edition, pages
Taylor & Francis, 2012
Keyword
Least Absolute Deviation, Ridge Regression, Robust Estimators
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-17462 (URN)
Available from: 2012-08-30 Created: 2012-01-28 Last updated: 2017-12-08Bibliographically approved
5. On the least absolute deviations method for ridge estimation of SURE models
Open this publication in new window or tab >>On the least absolute deviations method for ridge estimation of SURE models
2012 (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.

Keyword
SURE Models, LAD Estimation, Ridge Regression, Efficiency, Robustness
National Category
Economics and Business
Identifiers
urn:nbn:se:hj:diva-19682 (URN)10.1080/03610926.2012.755203 (DOI)
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2017-12-07

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