Heavy-Tailed Density Estimation
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.
Type
Journal articleSubject
Logistic Gaussian processesPosterior contraction
Regular variation
Semiparametric estimation
Tail index estimation
Permalink
https://hdl.handle.net/10161/26277Published Version (Please cite this version)
10.1080/01621459.2022.2104727Publication Info
Tokdar, ST; Jiang, S; & Cunningham, EL (2022). Heavy-Tailed Density Estimation. Journal of the American Statistical Association. pp. 1-13. 10.1080/01621459.2022.2104727. Retrieved from https://hdl.handle.net/10161/26277.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Surya Tapas Tokdar
Professor of Statistical Science

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