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Grama, Ion; Spokoiny, Vladimir

Statistics of extremes by oracle estimation. (English) Zbl 1282.62131

Ann. Stat. 36, No. 4, 1619-1648 (2008).
Summary: 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.

Cited in 10 Documents

MSC:

62G32 Statistics of extreme values; tail inference
62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation

Keywords:

nonparametric adaptive estimation; extreme values; Hill estimator; probabilities of rare events; high quantiles
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References:

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