Testing homogeneity of a parameter matrix with some rows constrained by synchronized order restrictions

Paper presented to the 6th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held at the Hughes Metropolitan Complex, Wichita State University, April 23, 2010.Research completed at the Department of Mathematics and Statistics, College of Liberal Arts and SciencesA multivariate linear regression model Y~N (βM',Σ) is considered where some of the rows in the coefficient matrix β are constrained by synchronized order restrictions. A test scheme is derived for the homogeneity of the coefficient matrix using the likelihood-ratio test procedure under the assumption that the coefficient matrix Σ is known. When Σ is unknown, a new ad-hoc test statistic TH(Y) is proposed by replacing the covariance matrix with its estimator, where H is a non-empty subset of the row-index space {1,2,...,p}.The properties of TH(Y) are studied and a theorem is also stated on the distribution of TH(Y) which eventually helps us to estimate p-values using the Monte-Carlo method by simulation