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In this paper, we study the estimation of parameters for g-and-h distributions. These distributions find applications in modeling highly skewed and fat-tailed data, like extreme losses in the banking and insurance sector. We first introduce two estimation methods: a numerical maximum likelihood technique, and an indirect inference approach with a bootstrap weighting scheme. In a realistic simulation study, we show that indirect inference is computationally more efficient and provides better estimates than the maximum likelihood method in the case of extreme features in the data. Empirical illustrations on insurance and operational losses illustrate these findings. [ABSTRACT FROM AUTHOR]

The g-and-h distribution is able to handle well the complex behavior of loss data and applied to operational losses suggests that indirect inference estimators of VaR outperform quantile-based estimators [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]