Bootstrap Bartlett Adjustment on decomposed variance-covariance matrix of seemingly unrelated regression model

Abstract

We investigated hypothesis testing in Seemingly Unrelated Regression (SUR) using Log Likelihood Ratio (LLR) test. The asymptotic distribution of this statistic is well documented in literature to have substantial inaccuracy by an order of magnitude leading to the rejection of too many true null hypotheses. Bartlett adjustment of Barndorff and Blaesild and Efron’s bootstrap methods were considered to provide more accurate significance level to the distribution. Simulation results from the partitioned variance-covariance matrix showed that the lower triangular matrix performed better than the upper triangular matrix. The Bartlett method of Barndorff and Blaesild provided better significance value than the bootstrap method.

Keywords: Bartlett Adjustment, Bootstrap, Generalised Least Squares, Likelihood Ratio Test, Maximum Likelihood, Triangular Matrices, Seemingly Unrelated Regression

AMS 2010 Mathematics Subject Classification: 62J05, 62F03