| In recent years there has been a significant amount of interest in developing tests that incorporate one-sided information. These tests have been shown to provide improved inference in a wide variety of situations, due to the fact that additional non-sample information is employed in their construction. In this paper, we investigate whether similar improvements are observed when we have non-sample information regarding the nuisance parameters in the testing problem. It is shown, under several realistic regularity conditions, that tests based on inequality constrained estimates of nuisance parameters and tests based on unconstrained estimates have identical asymptotic properties. For the case of small samples, however, Monte Carlo evidence presented suggests that the use of such non-sample information can lead to significant improvements in the average power of tests but, due to the bias of the inequality constrained estimator, worse power in certain parts of the parameter space. We then consider bootstrap methods that are currently available to deal with the bias and develop tests with good size properties and almost uniformly higher power. |