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水瓶公主 · 2024年05月05日

数量多，错误多

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2023100703000026

问题如下：

A risk analyst at an investment bank is examining how quantile estimators can be incorporated into the bank’s risk measures. The analyst focuses on how estimators are constructed and how their precision and usefulness are determined. Which of the following statements about quantile estimators is correct?

选项：

A.Each quantile in the loss distribution must have an equal weight when used to create a coherent risk measure.

B.The data and processes involved in estimating quantiles are different from those used to estimate coherent risk measures.

C.QQ plots are a useful tool to evaluate the precision of a quantile estimator.

D.Both the halving error and the standard error of a quantile estimator decrease as the number of quantiles used in the estimation process increases.

解释：

D is correct. The halving error and the standard error of a quantile estimator will both decrease as the number of slices, n, or quantiles, used in the process of estimating the risk measure increases. A is incorrect. Coherent risk measures can be created using sophisticated weighting functions and do not need to be equally weighted. B is incorrect. The building blocks of quantile estimation are essentially the same needed to estimate coherent risk measures. C is incorrect. QQ plots are a useful diagnostic tool when considering what kind of distribution might fit the profit and loss data. QQ plots are not used to analyze or evaluate quantile estimators.

D选项的意思没懂，之前的结论不是数量多错误多吗

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1 个答案

pzqa39 · 2024年05月05日

嗨，努力学习的PZer你好：


在估计过程中，不论是分半误差（halving error）还是分位数估计器的标准误差，都会随着用于估计的分位数数量增加而减少。

也就是说，当用于估算风险度量过程中切分的区间数量n（或者使用的分位数数量）增加时，分半误差和分位数估计器的标准误差都将减小。

解释：这里提到的两个概念解释如下：

  1. 分半误差（Halving Error）：这是一种衡量分位数估计不确定性的方法，尤其是在数据量有限或需要高效计算时采用的近似方法中。随着划分的区间（或分位数）增多，每个区间包含的数据点也会增多，从而减少了因数据分割不均导致的误差。
  2. 标准误差：这是衡量样本统计量（在这里是分位数）与总体参数之间差异的统计量，反映了估计的精度。标准误差越小，说明估计的稳定性越高，受随机抽样波动的影响越小。在分位数估计中，随着使用的分位数增多，每个分位数的估计会基于更多的数据信息，从而提高了估计的准确性，降低了标准误差。


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2024-10-13 10:45 1 · 回答