Rates of almost sure convergence of plug-in estimates for distortion risk measures
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Date
2010-03-02T13:33:16Z
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Abstract
In this article, we consider plug-in estimates for distortion risk measures as for
instance the Value-at-Risk, the Expected Shortfall or the Wang transform. We allow
for fairly general estimates of the underlying unknown distribution function (beyond
the classical empirical distribution function) to be plugged in the risk measure. We
establish strong consistency of the estimates, we investigate the rate of almost sure
convergence, and we study the small sample behavior by means of simulations.
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Keywords
risk measure, plug-in estimation, empirical distribution function, smoothing, censoring, Glivenko-Cantelli theorem for weighted errors