Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models
Statistics Theory
2014-09-18 v2 Statistics Theory
Abstract
We study the problem of constructing honest and adaptive confidence intervals for the tail coefficient in the 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.
Keywords
Cite
@article{arxiv.1312.2968,
title = {Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models},
author = {Alexandra Carpentier and Arlene K. H. Kim},
journal= {arXiv preprint arXiv:1312.2968},
year = {2014}
}