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.

Hill estimator, bias, stable distribution, tail index
dx.doi.org/10.1080/03610929608831726, hdl.handle.net/1765/12407
Communications in Statistics: Theory and Methods
Erasmus School of Economics

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