On the Favorable Estimation for Fitting Heavy Tailed Data

0342150 - ÚI 2011 RIV DE eng J - Journal Article
Stehlík, M. - Potocký, R. - Waldl, H. - Fabián, Zdeněk
On the Favorable Estimation for Fitting Heavy Tailed Data.
Computational Statistics. Roč. 25, č. 3 (2010), s. 485-503. ISSN 0943-4062. E-ISSN 1613-9658
Grant - others:ASO(SK) SK-0607-BA-018; VEGA(SK) 1/0077/09; 50p14(CZ-AT) AKTION; AKTION(CZ-AT) 54p13
Institutional research plan: CEZ:AV0Z10300504
Keywords : heavy-tailed distribution * exact likelihood ratio test * T-score moment estimator * insurance * Basel II
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 0.500, year: 2010

Assessment of heavy tailed data and its compound sums has many applications in insurance, auditing and operational risk capital assessment among others. In this paper, we compare the classical estimators (maximum likelihood, QQ and moment estimators) with the recently introduced robust estimators of “generalized median”, “trimmed mean” and estimators based on t-score moments. We derive the exact distribution of the likelihood ratio tests of homogeneity and simple hypothesis on the tail index of a two-parameter Pareto model. Such exact tests support the assessment of the performance of estimators. In particular, we discuss some problems that one can encounter when misemploying the log-normal assumption based methods supported by the Basel II framework. Real data and simulated examples illustrate the methods.
Permanent Link: http://hdl.handle.net/11104/0184964