This paper proposes tests that can be used to compare the accuracy of alternative density forecasts of a variable. The tests are also valid in the broader context of model selection based on out-of-sample predictive ability. We restrict attention to the case of density forecasts derived from non-nested parametric models, with known or estimated parameters. We propose asymptotic and bootstrap weighted likelihood ratio tests that focus power on different regions of the unconditional distribution of the variable, as a way to incorporate loss functions into the evaluation procedure. We show that the likelihood ratio test for non-nested hypotheses proposed by Vuong (1989) can be obtained in our framework. A Monte Carlo simulation and an empirical application to density forecasts of S&P500 daily returns conclude the paper.