Electronic Journal of Statistics

Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models

Alexandra Carpentier and Arlene K. H. Kim

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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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Electron. J. Statist., Volume 8, Number 2 (2014), 2066-2110.

First available in Project Euclid: 29 October 2014

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Confidence intervals minimax testing Pareto model extreme value theory


Carpentier, Alexandra; Kim, Arlene K. H. Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models. Electron. J. Statist. 8 (2014), no. 2, 2066--2110. doi:10.1214/14-EJS944. https://projecteuclid.org/euclid.ejs/1414588187

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