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Title: A stochastic approximation approach for parametric inference of intractable likelihood models Authors:  Wentao Li - The university of Manchester (United Kingdom) [presenting]
Abstract: For generative models with intractable likelihood, popular parametric inference methods include the synthetic likelihood (SL), the method of simulated moments and indirect inference. These methods can be treated as simulation-based variants of the generalized method of moments. Their computational cost mainly depends on the optimization scheme and the number of pseudo dataset simulations, $N$, used for one estimation of the theoretical moment. In order to study the impact of $N$, we use the framework of the generalized empirical likelihood to study the asymptotic properties of the above methods and a simulation-based version of the empirical likelihood estimator. It is shown that optimizers given by these methods are first-order equivalent when $N$ is fixed and as the data size goes to infinity. They are consistent and the asymptotic distribution depends on the distribution of the summary statistics. We also propose a mini-batched stochastic approximation algorithm to obtain the SL maximizer and its asymptotic variance estimator. Numerical studies show that the proposed algorithm is insensitive to the choice of $N$, and, compared to the commonly used synthetic-likelihood-based Metropolis-Hasting algorithm, computationally more efficient in obtaining accurate coverage probability over one order of magnitude.