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2014 Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models
Alexandra Carpentier, Arlene K. H. Kim
Electron. J. Statist. 8(2): 2066-2110 (2014). DOI: 10.1214/14-EJS944

Abstract

We study the problem of constructing uniform and adaptive confidence intervals for the tail coefficient in a second order Pareto model, when the second order coefficient is unknown. This problem is translated into a testing problem on the second order parameter. By constructing an appropriate model and an associated test statistic, we provide a uniform and adaptive confidence interval for the first order parameter. We also provide an almost matching lower bound, which proves that the result is minimax optimal up to a logarithmic factor.

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Alexandra Carpentier. Arlene K. H. Kim. "Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models." Electron. J. Statist. 8 (2) 2066 - 2110, 2014. https://doi.org/10.1214/14-EJS944

Information

Published: 2014
First available in Project Euclid: 29 October 2014

zbMATH: 1305.62198
MathSciNet: MR3273619
Digital Object Identifier: 10.1214/14-EJS944

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.8 • No. 2 • 2014
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