medium · FRM Part 2 Market Risk
A risk practitioner is using the Hill estimator to find the tail index of a heavy-tailed distribution. They plot the estimates hatxi for different values of k (the number of tail observations).
What is the practitioner looking for in this 'Hill plot' to select a reliable estimate?
- The value of k that minimizes the standard error of the estimate.
- The point where the estimate hatxi crosses zero, indicating the boundary between heavy and thin tails.
- A stable 'plateau' where the estimate hatxi does not change significantly as k varies.
- The value of k that corresponds exactly to the 95th percentile of the data.
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