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Abstract:
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In this work, we propose to use machine learning techniques to estimate parameters of complex models, for which standard likelihood estimation or Bayesian methods are not feasible. For instance, in high dimensions, inference for max-stable processes is extremely difficult, even with small data sets. Typical approaches rely on composite likelihoods, usually constructed from pairs of observations. However, these estimators imply a loss in efficiency for high dimensions, and classical likelihood theory cannot be applied since the independence assumed among the composite likelihood's component is usually not valid when the full likelihood is considered. Simulation from such models is usually more manageable than full likelihood computation. We propose to use data from simulations as input to an artificial neural network, whereas the output consists of the statistical parameters or distribution features. This methodology provides an alternative to classical likelihood approaches, with considerable improvements in accuracy and computational time. It serves as a proof-of-concept for machine learning in statistics and can be extended to other estimation problems.
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