A characteristic function-based approach to approximate maximum likelihood estimation. Issue 13 (3rd July 2018)

• Record Type: Journal Article
• Authors: Bee, M.; Trapin, L.
• Is Part Of: Communications in statistics. Volume 47:Issue 13(2018)
• Page Start: 3138
• Page End: 3160
• Publication Date: 2018-07-03
• Subjects: Characteristic function -- Intractable likelihood -- κ-Nearest neighbor entropy -- Summary statistics; 62F10 -- 62F99; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1348523
• Languages: English
• ISSNs: 0361-0926

Abstract

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.