Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models

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