Heavy-Tailed Density Estimation

dc.contributor.author

Tokdar, ST

dc.contributor.author

Jiang, S

dc.contributor.author

Cunningham, EL

dc.date.accessioned

2022-12-01T16:20:55Z

dc.date.available

2022-12-01T16:20:55Z

dc.date.issued

2022-01-01

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2022-12-01T16:20:54Z

dc.description.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.

dc.identifier.issn

0162-1459

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1537-274X

dc.identifier.uri

https://hdl.handle.net/10161/26277

dc.language

en

dc.publisher

Informa UK Limited

dc.relation.ispartof

Journal of the American Statistical Association

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10.1080/01621459.2022.2104727

dc.subject

Logistic Gaussian processes

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Posterior contraction

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Regular variation

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Semiparametric estimation

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Tail index estimation

dc.title

Heavy-Tailed Density Estimation

dc.type

Journal article

duke.contributor.orcid

Tokdar, ST|0000-0001-5162-1155

pubs.begin-page

1

pubs.end-page

13

pubs.organisational-group

Duke

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Trinity College of Arts & Sciences

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Statistical Science

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Institutes and Provost's Academic Units

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University Institutes and Centers

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Duke Institute for Brain Sciences

pubs.publication-status

Published

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