  Likelihood-free inference for simulator-based statistical models has recently
attracted a surge of interest, both in the machine learning and statistics
communities. The primary focus of these research fields 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 with big data where implicit asymptotic approximation of the
likelihood is expected to be accurate and can leverage computationally
efficient strategies. Here we derive a set of theoretical 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. 61
