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 dis turbances in the linear regression model that involves nuisance parame ters which cannot be eliminated by the usual invariance arguments. sco re-based tests, namely, Lagrange multiplier (LM) and locally most mean -powerful (LMMP) tests an derived from the marginal likelihood. Applic ations considered include (i) testing for random regression coefficien ts, (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 counterpart s. (C) 1997 Elsevier Science S.A.