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arXiv · 0808.0976

Statistics of extremes by oracle estimation

Ion Grama·Vladimir Spokoiny
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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. 2008-08-07. Statistics of extremes by oracle estimation. https://doi.org/10.1214/07-aos535

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