© Springer International Publishing Switzerland 2015. We outline an approach to statistical inference based on belief functions. For estimation, a consonant belief functions is constructed from the likelihood function. For prediction, the method is based on an equation linking the unobserved random quantity to be predicted, to the parameter and some underlying auxiliary variable with known distribution. The approach allows us to compute a predictive belief function that reflects both estimation and random uncertainties. Themethod is invariant to one-to-one transformations of the parameter and compatible with Bayesian inference, in the sense that it yields the same results when provided with the same information. It does not, however, require the user to provide prior probability distributions. The method is applied to stochastic frontier analysis with cross-sectional data. We demonstrate how predictive belief functions on inefficiencies can be constructed for this problem and used to assess the plausibility of various assertions.