科研之友
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摘要
We consider the problem of estimating the tail index alpha of a distribution satisfying a (alpha, beta) second-order Pareto-type condition, where beta is the second-order coefficient. When beta is available, it was previously proved that alpha can be estimated with the optimal rate n(-beta/(2 beta+1)). When beta is not available, estimating alpha with the optimal rate is challenging; so additional assumptions that imply the estimability of beta are usually made. We propose an adaptive estimator of alpha, and show that this. estimator attains the rate (n/log log n)(-beta/(2 beta+1)) without a priori knowledge of beta or additional assumptions. Moreover, we prove that a (log log n)(beta/(2 beta+1)) factor is unavoidable by obtaining the companion lower bound.
- 出版日期2015-7
