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Title: Approximate maximum likelihood estimation of the lognormal-GPD model with dynamic weights Authors:  Marco Bee - University of Trento (Italy) [presenting]
Abstract: Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is a difficult problem, mostly because of the need to evaluate an intractable normalizing constant numerically. In such a setup, simulation-based estimation methods are likely to work well. Accordingly, we employ Approximate maximum likelihood estimation (AMLE). This is a general approach that can be applied to a mixture of any component; we focus on the dynamic lognormal-GPD distribution, and use the empirical characteristic function as a summary statistics. In particular, we develop a hybrid procedure where the standard maximum likelihood is first employed to determine the bounds of the uniform priors of the parameters required as input for the AMLE method. Simulation experiments and a real-data application suggest that this approach yields a major improvement with respect to standard maximum likelihood estimation.