Fat tail distributions and local thin tail alternatives
The behaviour of the Hill estimator for the tail index of fat tailed distributions in the presence of local alternatives which have a thin tail is investigated. The converse problem is also briefly addressed. A local thin tail alternative can severely bias the Hill statistic. The relevance of this issue for the class of stable distributions is discussed. We conduct a small simulation study to support the analysis. In the conclusion it is argued that for moderate out of sample quantile analysis the problem of local alternatives may be less pressing.
|Keywords||Hill estimator, bias, stable distribution, tail index|
|Persistent URL||dx.doi.org/10.1080/03610929608831726, hdl.handle.net/1765/12407|
Gielens, G., Straetmans, S., & de Vries, C.G.. (1996). Fat tail distributions and local thin tail alternatives. Communications in Statistics: Theory and Methods, 705–710. doi:10.1080/03610929608831726