Heavy-Tailed Density Estimation

• 成果类型: Article
• 署名作者: Tokdar, Surya T.; Jiang, Sheng; Cunningham, Erika L.
• 署名单位: Duke University; University of California System; University of California Santa Cruz
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2104727
• 发表日期: 2024
• 页码: 163-175
• 关键词: posterior consistency; rates; CONVERGENCE; parameters; inference; priors; index

摘要

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.