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.

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Communications in Statistics: Theory and Methods
Erasmus School of Economics

Gielens, G., Straetmans, S., & de Vries, C. (1996). Fat tail distributions and local thin tail alternatives. Communications in Statistics: Theory and Methods, 705–710. doi:10.1080/03610929608831726