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The generalized sigmoidal quantile function.

Alan D Hutson1

  • 1Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, Buffalo, New York, USA.

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Summary
This summary is machine-generated.

This study introduces a novel sigmoidal quantile function estimator for improved nonparametric quantile estimation. This method enhances data extrapolation, benefiting small sample sizes and bootstrap resampling techniques.

Keywords:
BootstrapExpectilesHermitian quantile functionKernel quantile estimatorTail extrapolation

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Area of Science:

  • Statistics
  • Nonparametric Statistics
  • Econometrics

Background:

  • Quantile estimation is crucial in statistical analysis.
  • Existing methods may face limitations with small sample sizes or require extrapolation.
  • Nonparametric methods offer flexibility but can be complex.

Purpose of the Study:

  • Introduce a new smooth nonparametric quantile function estimator.
  • Develop a generalized sigmoidal quantile function estimator.
  • Create a hybrid estimator combining existing and new methods.

Main Methods:

  • Utilized a newly defined generalized expectile function.
  • Developed a sigmoidal quantile function estimator.
  • Combined kernel and sigmoidal estimators for a hybrid approach.

Main Results:

  • The sigmoidal quantile function estimator allows for quantile estimation beyond the data range.
  • This extrapolation capability is particularly useful for smaller sample sizes.
  • The hybrid estimator integrates optimal properties of classic and novel methods.

Conclusions:

  • The proposed sigmoidal quantile function estimator offers advantages in extrapolation.
  • This method can improve standard bootstrap smoothing and resampling.
  • The generalized sigmoidal function provides a flexible tool for quantile estimation.