Classical methods of parameter estimation usually imply the minimisation of an objective function, that measures the error between some observations and the results obtained by a numerical model. In the presence of random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced. In this paper, we are going to present how to take into account those uncertainties by defining a family of calibration objectives based on the notion of relative-regret with respect to the best attainable performance given the uncertainties and compare it with the minimum in the mean sense, and the minimum of variance.