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

When choosing the threshold u in a POT analysis, what is the main trade-off?

Raising the threshold makes the GPD approximation more valid, reducing bias, but leaves fewer exceedances and so raises the variance of parameter estimates. Lowering it does the opposite, giving more data but risking bias.

  1. AA high u reduces bias but increases variance because fewer exceedances remainCorrect
  2. BA high u increases bias and reduces variance because the GPD fits worse
  3. CA low u always gives an exact GPD fit with no bias
  4. DThreshold choice has no effect on the estimated shape parameter
  5. A low u reduces variance and bias together

Explanation

A higher threshold makes the GPD approximation more accurate (lower bias) but leaves fewer data points, so estimates are more variable. A lower threshold gives more data but risks bias because the GPD is only a limiting model.

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