Ponente
Descripción
Quantiles and expectiles play a crucial role in both statistics and operations research. While the main attention has been focused on the estimators of quantiles, expectiles were set surprisingly apart from the main stream of interest. In the lecture we contrast the two approaches and show how to get quantiles from a fine grid of expectiles. We compare such ``quantiles from expectiles'' with direct quantile estimates regarding efficiency, especially when using Bernstein polynomials to that purpose. An application of the suggested estimators in the field of steady state simulations, that play a crucial role in accurately evaluating the long run performance and risk of complex systems or analyses of financial portfolios, will be given. Aside that, we will also show its use for the Value-at-Risk and expectile based Value-at-Risk estimation, and expected shortfall.
