Nonparametric Estimation of CVaR and Expected Shortfall

Summary

The document asks whether estimating conditional value at risk, also called expected shortfall, requires different treatment from estimating other properties of a random variable. It specifically names histogram and kernel methods and asks whether nonparametric estimators for CVaR can be consistent.

It does not provide an estimator, derivation, comparison, or empirical evidence, so it serves as a focused research question rather than an instructional treatment. The central issue is that CVaR depends on a tail region selected by a quantile, which makes sample size and tail behavior relevant to estimation. Any answer would need to state assumptions about the underlying distribution and the confidence level, as well as what form of consistency is intended. The document itself leaves these conditions unspecified and offers no conclusion about which methods work.

Key ideas

• The document asks whether CVaR estimation differs from estimation of other distributional quantities.
• Histogram and kernel approaches are raised as candidate nonparametric methods.
• The question specifically asks whether nonparametric CVaR estimators can be consistent.
• No estimator, assumptions, comparisons, or evidence are supplied.

Tags

# Non-parametric estimator - CVaR / Expected shortfall


# Non-parametric estimator - CVaR / Expected shortfall












Is the estimation of the CVaR using known non-parametric methods (histogram, kernels) different than the estimation of any other R.V.?

If the answer is yes, I am interested to know whether there are some non-parametric methods for CVaR estimation which are also consistent.

Thanks

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.