On Median and Ridge Estimation of SURE Models

Abstract: 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.