文章基本信息

标题：Adaptive confidence intervals for the tail coefficient in a wide second order class of Pareto models
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作者：Alexandra Carpentier ; Arlene K. H. Kim
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2014
卷号：8
期号：2
页码：2066-2110
DOI：10.1214/14-EJS944
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.