Statistics of extremes by oracle estimation
The Annals of Statistics · 2008 · Volume 36 · Issue 4
Abstract
We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing procedure. Our main result is an oracle type inequality for the Kullback–Leibler loss.
Keywords
62G05, 62G08, 62G32, Extreme values, high quantiles, Hill estimator, Nonparametric adaptive estimation, probabilities of rare events
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