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Answer: Both the halving error and the standard error of a quantile estimator decrease as the number of quantiles used in the estimation process increases.
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. This is because increasing the number of quantiles provides more information and reduces the estimation error. Option A is incorrect because coherent risk measures can be created using sophisticated weighting functions and do not require equal weighting. Option B is incorrect as the processes and data used for estimating quantiles are essentially the same as those needed for estimating coherent risk measures. Option C is incorrect because QQ plots are used to assess the fit of a distribution to the data, not to evaluate quantile estimators.
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An investment bank's risk analyst is examining how to incorporate quantile estimators into the organization's risk assessment models. Quantile estimators are statistical tools used to estimate specific quantiles within a data set, such as the median or various percentiles, which are crucial in understanding the distribution and risk characteristics of financial returns. The analyst is particularly interested in the methods used to construct these quantile estimators and the standards by which their accuracy and effectiveness are judged. 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.