Locally optimal one-sided tests for multiparameter hypotheses

Recently, there has been an increased awareness of the one-sided nature of many econometric testing problems. This paper constructs a locally most mean powerful (LMMP) test of a silnple null hypothesis against a lnultiparameter one-sided alternative. The resultant test statistic is the sum of the scores evaluated at the null hypothesis. This makes it easy to apply both with and without nuisance parameters. In the case of the linear regression model, invariance arguments can be used to deal with nuisance parameters allowing the construction of exact tests. Applications considered in the context of the linear regression model include joint one-sided testing for non-zero regression coefficients, autoregressive disturbances, heteroscedastic disturbances, random regression coefficients and variance components..