Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models
Tsz Chai Fung · Insurance Mathematics and Economics · 2022
Insurance claim severity data are characterized by complex distributional phenomenons, where flexible density estimation tools such as the finite mixture models (FMM) are necessary. However, maximum likelihood estimations (MLE) often produce unstable tail estimates for the FMM. Motivated by this challenge, this article presents a maximum weighted likelihood estimator (MWLE) for robust estimations of heavy-tailed FMM. Under some regularity conditions , the proposed MWLE is consistent and asymptotically normal. Since the MWLE has a probabilistic interpretation, we are able to develop two distinctive versions of the Generalized Expectation-Maximization (GEM) algorithm to estimate the MWLE parameters more efficiently and reliably than the standard gradient-based algorithms. We apply the proposed MWLE to two simulation studies and a real motor insurance dataset to demonstrate that it better extrapolates the extreme losses than the MLE, without sacrificing the flexibility of the FMM in capturing the small attritional claims.