The generalized sigmoidal quantile function

In this note we introduce a new smooth nonparametric quantile function estimator based on a newly defined generalized expectile function and termed the sigmoidal quantile function estimator. We also introduce a hybrid quantile function estimator, which combines the optimal properties of the classic...

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Published in:	Communications in statistics. Simulation and computation Vol. 53; no. 2; pp. 799 - 813
Main Author:	Hutson, Alan D.
Format:	Journal Article
Language:	English
Published:	United States Taylor & Francis 2024 Taylor & Francis Ltd
Subjects:	Bootstrap Expectiles Hermitian quantile function Kernel quantile estimator Quantiles Resampling Tail extrapolation Bootstrap Kernel quantile estimator Tail extrapolation Expectiles Hermitian quantile function
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Abstract	In this note we introduce a new smooth nonparametric quantile function estimator based on a newly defined generalized expectile function and termed the sigmoidal quantile function estimator. We also introduce a hybrid quantile function estimator, which combines the optimal properties of the classic kernel quantile function estimator with our new generalized sigmoidal quantile function estimator. The generalized sigmoidal quantile function can estimate quantiles beyond the range of the data, which is important for certain applications given smaller sample sizes. This property of extrapolation is illustrated in order to improve standard bootstrap smoothing resampling methods.
AbstractList	In this note we introduce a new smooth nonparametric quantile function estimator based on a newly defined generalized expectile function and termed the sigmoidal quantile function estimator. We also introduce a hybrid quantile function estimator, which combines the optimal properties of the classic kernel quantile function estimator with our new generalized sigmoidal quantile function estimator. The generalized sigmoidal quantile function can estimate quantiles beyond the range of the data, which is important for certain applications given smaller sample sizes. This property of extrapolation is illustrated in order to improve standard bootstrap smoothing resampling methods.
Author	Hutson, Alan D.
Author_xml	– sequence: 1 givenname: Alan D. surname: Hutson fullname: Hutson, Alan D. organization: Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute
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SubjectTerms	Bootstrap Expectiles Hermitian quantile function Kernel quantile estimator Quantiles Resampling Tail extrapolation
Title	The generalized sigmoidal quantile function
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