Heavy-Tailed Density Estimation
Heavy-Tailed Density Estimation
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DOI：
10.1080/01621459.2022.2104727
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发表时间：
2022-07
影响因子：
3.7
通讯作者：
S. Tokdar;Sheng Jiang;Erika L Cunningham
中科院分区：
文献类型：
--
作者：
S. Tokdar;Sheng Jiang;Erika L Cunningham
摘要提出并研究了一种新的统计方法，用于在弱光滑假设下估计重尾密度。重尾分布的统计分析容易受到分布尾部的稀疏信息被大量不相关特征冲走的问题的影响。建议的贝叶斯方法避免了这个问题，通过一个仔细指定的半参数先验分布的平滑和尾部正则化，并能够一致地估计密度函数及其尾部指数在接近最小最大最优收缩率。联合，似然驱动估计的批量和尾部，以帮助提高不确定性评估估计尾部指数参数，并提供更准确和可靠的估计相比，阈值方法的高尾分位数。本文的补充材料可在网上查阅。
Abstract A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk. The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularization through a carefully specified semiparametric prior distribution, and is able to consistently estimate both the density function and its tail index at near minimax optimal rates of contraction. A joint, likelihood driven estimation of the bulk and the tail is shown to help improve uncertainty assessment in estimating the tail index parameter and offer more accurate and reliable estimates of the high tail quantiles compared to thresholding methods. Supplementary materials for this article are available online.