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A characteristic function-based approach to approximate maximum likelihood estimation

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  • M. Bee
  • L. Trapin

Abstract

The choice of the summary statistics in approximate maximum likelihood is often a crucial issue. We develop a criterion for choosing the most effective summary statistic and then focus on the empirical characteristic function. In the iid setting, the approximating posterior distribution converges to the approximate distribution of the parameters conditional upon the empirical characteristic function. Simulation experiments suggest that the method is often preferable to numerical maximum likelihood. In a time-series framework, no optimality result can be proved, but the simulations indicate that the method is effective in small samples.

Suggested Citation

  • M. Bee & L. Trapin, 2018. "A characteristic function-based approach to approximate maximum likelihood estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(13), pages 3138-3160, July.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:13:p:3138-3160
    DOI: 10.1080/03610926.2017.1348523
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    Cited by:

    1. Marcin Pitera & Aleksei Chechkin & Agnieszka Wyłomańska, 2022. "Goodness-of-fit test for $$\alpha$$ α -stable distribution based on the quantile conditional variance statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 387-424, June.
    2. Marco Bee, 2022. "The truncated g-and-h distribution: estimation and application to loss modeling," Computational Statistics, Springer, vol. 37(4), pages 1771-1794, September.

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