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Answer: QQ plots are a useful tool to evaluate the precision of a quantile estimator.
## Explanation Let's analyze each option: **A. Incorrect** - When creating coherent risk measures, quantiles do NOT need to have equal weights. In fact, coherent risk measures like Expected Shortfall (ES) give different weights to different quantiles in the tail of the distribution. **B. Incorrect** - The data and processes involved in estimating quantiles are essentially the same as those used to estimate coherent risk measures. Both rely on the same underlying loss distribution data and estimation methodologies. **C. Correct** - QQ plots (Quantile-Quantile plots) are indeed useful tools for evaluating the precision and accuracy of quantile estimators. They compare the quantiles of the estimated distribution against theoretical quantiles or quantiles from another distribution to assess goodness-of-fit. **D. Incorrect** - While standard error may decrease with more quantiles (due to more data points), halving error does not necessarily decrease. Halving error refers to the error in estimating the median, and increasing the number of quantiles doesn't necessarily improve median estimation. Therefore, option C is the correct statement about quantile estimators.
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Which of the following statements about quantile estimators is correct?
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.