Electronic Journal of Statistics

A simple approach to maximum intractable likelihood estimation

F. J. Rubio and Adam M. Johansen

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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.

Article information

Electron. J. Statist., Volume 7 (2013), 1632-1654.

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Approximate Bayesian Computation density estimation maximum likelihood estimation Monte Carlo methods


Rubio, F. J.; Johansen, Adam M. A simple approach to maximum intractable likelihood estimation. Electron. J. Statist. 7 (2013), 1632--1654. doi:10.1214/13-EJS819. https://projecteuclid.org/euclid.ejs/1371649229

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