Does anyone have experience of conflicting results when using the Pickand method and Hill method to estimate the tail index for the same data set?
i.e. E > 0 under Pickand and E < 0 under Hill method.
Is it possible?
To emphasize this point, remember that the use of boxes of side length r E → 0 as E → ∞, which measure the length of a form of E (rn) ⋅ rn as n → ∞, and we measure the area of E (rn) rn ⋅ 2 when n → ∞
Hill estimator is always positive, but Pickands estimator can lead to positive or negative values. So, if the true extreme-value index is negative, it is likely that you will obtain Pickands 0.
stephane
Thank you, Stephane.
If that is the case, how can we reconcile the different results?
If Pickans estimator gives a negative value, then you can also compare the result with other estimators making no assumption on the sign on the extreme value index: maximum likelihood, method of moments, ... If all of them yield a negative value, you should not use Hill estimator which is limited to the positive case.
you can also have a look at the confidence intervals to see if they include positive values or not.
i hope this helps,
Stephane
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