Statistics of extremes by oracle estimation

Ion Grama; Vladimir Spokoiny

doi:10.1214/07-AOS535

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August 2008 Statistics of extremes by oracle estimation

Ion Grama, Vladimir Spokoiny

Ann. Statist. 36(4): 1619-1648 (August 2008). DOI: 10.1214/07-AOS535

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.

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Ion Grama. Vladimir Spokoiny. "Statistics of extremes by oracle estimation." Ann. Statist. 36 (4) 1619 - 1648, August 2008. https://doi.org/10.1214/07-AOS535