NO.PZ2023100703000034
问题如下：
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?选项：
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.
解释：
A is correct. The regression method is the easiest method to apply, and the recovery of least squares estimates of the EV parameters from a regression is straightforward. The first step in applying the regression method is to order the sample of extreme values from lowest to highest. B is incorrect. The use of an arbitrary (not random) number would correctly describe the Hill estimator, which is used in semi-parametric estimation method. However, this would still be an incorrect answer to this specific question. C is incorrect. The main challenge with the semi-parametric method (not the moment-based method) is choosing the number of observations to include in the tail, as the parameter estimates can be sensitive to this number. D is incorrect. The most popular semi-parametric estimation method is the Hill estimator, which is known to be consistent and asymptotically normal.1.最小二乘和EVT的关系是什么 2.EVT的两种方法（POT＆GEV）都是semi-parametric approach吗
