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The generalized sigmoidal quantile function
1Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, Buffalo, New York, USA.
Communications in Statistics: Simulation and Computation
|March 25, 2024
Summary
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.
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.
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