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A simple approach to maximum intractable likelihood estimation. (English) Zbl 1327.62075
Summary: Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then maximised is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios.

MSC:
62E17 Approximations to statistical distributions (nonasymptotic)
62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62G07 Density estimation
65C05 Monte Carlo methods
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