Beta kernel quantile estimators of heavy-tailed loss distributions

Arthur Charpentier (1) , Abder Oulidi (2)

1 CREM - Centre de recherche en économie et management
2 MAI - Mathématiques Appliquées et Informatique

In this paper we suggest several nonparametric quantile estimators based on Beta kernel. They are applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte Carlo based study has shown that those estimators improve the efficiency of the traditional ones, not only for light tailed distributions, but also for heavy tailed, when the probability level is close to 1. We also compare these estimators with the Extreme Value Theory Quantile applied to Danish data on large fire insurance losses.

Mots clés: Beta kernels; Champernowne distribution; Loss distributions; Quantile estimation; Transformed kernel; Value-at-risk

Domaines: Economies et finances

Arthur Charpentier, Abder Oulidi. Beta kernel quantile estimators of heavy-tailed loss distributions. Statistics and Computing, 2010, 20 (1), pp.35-55. ⟨10.1007/s11222-009-9114-2⟩. ⟨halshs-00425566⟩