Likelihood-free inference for simulator-based statistical models has recently attracted an interest, both in the machine learning and statistics. The primary focus of has been to approximate the posterior distribution of model parameters, either by various types of Monte Carlo sampling algorithms or deep neural network -based surrogate models. Frequentist inference for simulator-based models has been given much less attention to date, despite that it would be particularly amenable to applications, where implicit asymptotic approximation of the likelihood is expected to be accurate and can leverage computationally efficient strategies. Here we derive a set of results to enable estimation, hypothesis testing and construction of confidence intervals for model parameters using asymptotic properties of the Jensen–Shannon divergence. Such asymptotic approximation offers a rapid alternative to more computation-intensive approaches and can be attractive for diverse applications of simulator-based models.