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Optimal bandwidth estimators of kernel density functionals for contaminated data.

Necla Gündüz1, Celal Aydın1

  • 1Faculty of Science, Department of Statistics, Gazi University, Ankara, TURKEY.

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|June 16, 2022
PubMed
Summary

This study introduces Cauchy-scale estimators as an alternative to normal-scale estimators for bandwidth selection in kernel density estimation. The proposed method demonstrates lower variance in contaminated data, improving density estimation accuracy.

Keywords:
62G0562G07Bandwidthcontaminated datadensity estimationdensity functionalskernel smoothing

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Area of Science:

  • Statistics
  • Data Science

Background:

  • Kernel density estimation (KDE) is a non-parametric method to estimate probability density functions.
  • Preliminary bandwidth selection is critical for accurate KDE, often relying on normal-scale estimators assuming normal data distributions.

Purpose of the Study:

  • To explore and characterize kernel density functionals within the location-scale family.
  • To introduce and evaluate Cauchy-scale estimators as an alternative to normal-scale estimators for preliminary bandwidth selection.
  • To assess the performance of bandwidth estimators under various contamination levels.

Main Methods:

  • Simulation-based exploration of kernel density functionals.
  • Development and application of Cauchy-scale estimators for bandwidth selection.
  • Comparative analysis of sampling distributions for normal- and Cauchy-scale bandwidth estimators.
  • Case study involving simulation of contaminated normal distributions.

Main Results:

  • The proposed Cauchy-scale estimators exhibit lower variance compared to traditional normal-scale estimators, particularly for mixture and contaminated data.
  • Simulation results indicate improved robustness and accuracy of the Cauchy-scale approach in density estimation.
  • The findings were validated through applications on a real-world dataset, showing consistency with simulation outcomes.

Conclusions:

  • Cauchy-scale estimators offer a robust alternative for preliminary bandwidth selection in kernel density estimation, especially when data deviates from normality or contains contamination.
  • This approach enhances the reliability of density estimation in practical scenarios with imperfect data.
  • The study contributes a valuable method for improving the accuracy and stability of kernel density estimation.