Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and demonstrate their robustness to potential model misspecification. Notably, these properties are established by circumventing the use of concentration inequalities and empirical process theory. We provide an illustration of this approach to the problem of estimating the intensity of a Poisson process.