Highly accurate likelihood analysis for the seemingly unrelated regression problem

The linear and nonlinear seemingly unrelated regression problem with general error distribution is analyzed using recent likelihood theory that arguably provides the definitive distribution for assessing a scalar parameter; this involves implicit but well defined conditioning and marginalization for determining intrinsic measures of departure. Highly accurate p-values are obtained for the key difference between two regression coefficients of central interest. The p-value gives the statistical position of the data with respect to the key parameter. The theory and the results indicate that this methodology provides substantial improvement on first-order likelihood procedures, both in distributional accuracy, and in precise measurement of the key parameter.