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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory

In the peaks-over-threshold method, an analyst chooses a threshold that is set too low. What is the most likely consequence?

A threshold that is too low brings in many observations that are not in the tail, so the GPD approximation is poor and estimates are biased, although variance is lower. Too few exceedances and high variance result from a threshold set too high.

  1. AToo few exceedances, giving high variance in parameter estimates
  2. BBias, because the GPD approximation may not hold for the many included observationsCorrect
  3. CNo effect, since the GPD is valid for any threshold
  4. DThe shape parameter must equal zero
  5. The estimates become unbiased with minimum variance

Explanation

The GPD result is asymptotic for high thresholds. A low threshold includes many observations, which lowers variance but introduces bias as the approximation fails. Too few exceedances arise from a threshold that is too high, not too low.

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