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Answer: The regression method uses an ordered sample of losses to obtain least squares estimates of the EV parameters.
## Explanation **A is correct.** The regression method is indeed the easiest method to apply for estimating extreme value parameters, and it involves using an ordered sample of losses to obtain least squares estimates. The process begins by ordering the sample of extreme values from lowest to highest, then applying regression techniques to estimate the EV parameters. **B is incorrect.** The description provided actually refers to the Hill estimator used in semi-parametric estimation, not the maximum-likelihood method. The Hill estimator uses an arbitrary (not random) number of the most extreme observations. **C is incorrect.** The challenge of choosing the number of observations that minimizes the mean-squared-error loss function is actually associated with the semi-parametric method, not the moment-based method. **D is incorrect.** The Hill estimator, which is the most popular semi-parametric estimation method, is actually known to be both consistent and asymptotically normal, contrary to what this statement claims. This question tests understanding of different methods for estimating extreme value parameters in extreme value theory, including their specific mechanics and characteristics.
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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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