Median regression for SUR models with the same explanatory variables in each equation

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.     

Modified Ridge Parameters for Seemingly Unrelated Regression Model

In this article, we modify a number of new biased estimators of seemingly unrelated regression (SUR) parameters which are developed by Alkhamisi and Shukur (2008 Alkhamisi , M. A. , Shukur , G. ( 2008 ). Developing ridge parameters for SUR model . Commun. Statist. Theor. Meth. 37 ( 4 ): 544 – 564 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), AS, when the explanatory variables are affected by multicollinearity. Nine estimators of the ridge parameters have been modified and compared in terms of the trace mean squared error (TMSE) and (PR) criterion. The results from this extended study are the also compared with those founded by AS. A simulation study has been conducted to compare the performance of the modified estimators of the ridge parameters. The results showed that under certain conditions the performance of the multivariate ridge regression estimators based on SUR ridge R _MSmax is superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high, the unbiased SUR, estimator produces a smaller TMSEs.     

Seemingly unrelated regressions with covariance matrix of cross-equation ridge regression residuals

Generalized least squares estimation of a system of seemingly unrelated regressions is usually a two-stage method: (1) estimation of cross-equation covariance matrix from ordinary least squares residuals for transforming data, and (2) application of least squares on transformed data. In presence of multicollinearity problem, conventionally ridge regression is applied at stage 2. We investigate the usage of ridge residuals at stage 1, and show analytically that the covariance matrix based on the least squares residuals does not always result in more efficient estimator. A simulation study and an application to a system of firms' gross investment support our finding.     

Developing ridge estimation method for median regression

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.