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) are necessary. However, maximum likelihood estimations (MLE) often produce unstable tail estimates for the FMM. Motivated by this cha...

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Vydáno v:Insurance, mathematics & economics Ročník 107; s. 180 - 198
Hlavní autor: Fung, Tsz Chai
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.11.2022
Témata:
Generalized expectation-maximization algorithm
M-estimator
Multimodal distribution
Random truncation
Regularly varying function
Random truncation
C13
Multimodal distribution
G22
M-estimator
Regularly varying function
C18
Generalized expectation-maximization algorithm
ISSN:0167-6687, 1873-5959
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Popis
Shrnutí: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2022.08.008