Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters

This paper is concerned with tests of the covariance matrix of the disturbances in the linear regression model that involves nuisance parameters which cannot be eliminated by the usual invariance arguments. Score-based tests, namely, Lagrange multiplier (LM) and locally most mean-powerful (LMMP) tests are derived from the marginal likelihood. Applications considered include (i) testing for random regression coefficients, (ii) testing for second-order autoregressive (AR(2)) disturbances and (iii) testing for ARMA (1.1) disturbances, each in the presence of AR(1) disturbances. An empirical size and power comparison shows that the new tests typically have more accurate asymptotic critical values and slightly more power than their respective conventional counterparts.