COMPARISON OF BOOTSTRAP AND ASYMPTOTIC APPROXIMATIONS TO THE DISTRIBUTION OF A HEAVY-TAILED MEAN
COMPARISON OF BOOTSTRAP AND ASYMPTOTIC APPROXIMATIONS TO THE DISTRIBUTION OF A HEAVY-TAILED MEAN
复制标题
DOI：
--
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
P. Hall;Bing-Yi Jing
中科院分区：
文献类型：
--
作者：
P. Hall;Bing-Yi Jing
众所周知，对于重尾分布，自举可能导致样本平均值分布的不一致估计;并且这种困难可以通过使用所谓的“子样本自举”来克服，其中自举重新采样的大小比样本的大小小一个数量级。自然地，人们可能会问，在经典问题中，应用于重尾分布的自助法是否比渐近方法更准确地近似样本均值的分布。我们表明，一般来说，它没有。在一类重要的问题中，子样本自举比渐近方法表现得更差，即使子样本大小是最佳选择。与Richardson外推相关的技术，有效地子样本自举和渐近方法之间的交叉，在某些情况下（但不是所有情况下）比任何一种方法都好。
It is well-know that for heavy-tailed distributions the bootstrap can lead to inconsistent estimation of the distribution of the sample mean; and that this difficulty may be overcome by using the so-called "subsample bootstrap", where the size of a bootstrap resample is an order of magnitude smaller than that of the sample. Naturally, one might ask whether, as in classical problems, the bootstrap applied to heavy-tailed distributions produces more accurate approximations to the distribution of the sample mean than do asymptotic methods. We show that, generally speaking, it does not. In an important class of problems, the subsample bootstrap performs more poorly than asymptotic methods, even if the subsample size is chosen optimally. A technique related to Richardson extrapolation, effec- tively a cross between the subsample bootstrap and asymptotic methods, performs better than either approach in some, but not all, circumstances.