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Likelihood-free inference for simulator-based statistical models has recentlyattracted a surge of interest, both in the machine learning and statisticscommunities. The primary focus of these research fields has been to approximatethe posterior distribution of model parameters, either by various types ofMonte Carlo sampling algorithms or deep neural network -based surrogate models.Frequentist inference for simulator-based models has been given much lessattention to date, despite that it would be particularly amenable toapplications with big data where implicit asymptotic approximation of thelikelihood is expected to be accurate and can leverage computationallyefficient strategies. Here we derive a set of theoretical results to enableestimation, hypothesis testing and construction of confidence intervals formodel parameters using asymptotic properties of the Jensen--Shannon divergence.Such asymptotic approximation offers a rapid alternative to morecomputation-intensive approaches and can be attractive for diverse applicationsof simulator-based models. 61

Nonparametric likelihood-free inference with Jensen-Shannon divergence for simulator-based models with categorical output