Statistics of extremes by oracle estimation
Ion Grama, Vladimir Spokoiny
TL;DR
This paper introduces an oracle estimation method for the excess distribution function using Pareto law fitting, with a stagewise testing procedure and an oracle inequality for Kullback-Leibler loss.
Contribution
It proposes a novel selection rule for the excess distribution function location based on stagewise lack-of-fit testing, advancing statistical methods for extreme value analysis.
Findings
Provides an oracle inequality for Kullback-Leibler loss.
Develops a stagewise testing procedure for excess distribution function.
Offers a new approximation method using Pareto law fitting.
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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