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Answer: The regression method uses an ordered sample of losses to obtain least squares estimates of the EV parameters.
## Explanation **Correct Answer: A** The regression method for estimating extreme value parameters indeed uses an ordered sample of losses and applies least squares estimation to obtain the parameters. This method involves ordering the extreme observations and fitting a regression line to estimate the tail parameters. **Analysis of Other Options:** - **B**: Incorrect - The maximum-likelihood method does not use the average of extreme observations. Instead, it maximizes the likelihood function based on the entire sample or the extreme observations to estimate parameters. - **C**: Incorrect - While choosing the number of observations is important in moment-based methods, the main challenge is typically related to the sensitivity of estimates to the threshold choice and the stability of parameter estimates. - **D**: Incorrect - The Hill estimator in semi-parametric estimation is actually consistent and asymptotically normal under certain regularity conditions, making this statement false. **Key Points:** - The regression method is a valid approach for EVT parameter estimation - It relies on ordered extreme observations and least squares regression - This method is particularly useful when dealing with operational loss data where extreme values are of primary concern - The ordered nature of the sample allows for proper tail modeling in EVT applications
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Q-26. A risk analyst at an investment bank is evaluating the bank's application of extreme value theory (EVT) in managing financial risks. The analyst compares different methods of estimating extreme value (EV) parameters for the bank's operational loss distribution and examines the mechanics of each method, as well as their advantages and disadvantages. Which of the following statements regarding a method used for estimating EV parameters is correct?
A
The regression method uses an ordered sample of losses to obtain least squares estimates of the EV parameters.
B
The maximum-likelihood method uses the average of a random number of the most extreme observations to estimate EV parameters.
C
The main challenge associated with the moment-based method is choosing the number of observations that minimizes the mean-squared-error loss function.
D
A drawback of the semi-parametric estimation method is that the Hill estimator is neither consistent nor asymptotically normal.
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