On bias reduction for probability density function estimation based on a kernel estimator

Document Type : Original Scientific Paper

Authors

1 Department of Statistics, Payame Noor University, Tehran, Iran

2 Department of Mathematics and Statistics, Sa.C., Islamic Azad University, Sanandaj, Iran

Abstract

The probability density function is a fundamental concept in statistics‎. ‎This study focuses on estimating the probability density function using nonparametric kernel methods. ‎Initially‎, ‎the usual kernel method is introduced‎. ‎Subsequently‎, ‎we present the two new estimates of the probability density function‎, ‎termed the biased reduced kernel estimate‎, ‎the repeat of the biased reduced kernel estimate, and the proposed biased reduced kernel estimate obtained by subtracting the bias value from the kernel estimator‎. ‎The paper explores theoretical properties, including the selection of the smoothness parameter, bias, variance, and mean squared error of the proposed estimator. ‎The accuracy of the biased reduced kernel estimate is scrutinized through Monte Carlo simulations‎. ‎Moreover‎, ‎the mentioned methods were employed using the five real datasets‎. ‎The findings reveal that the proposed biased reduced kernel method exhibits a further reduction in bias compared to the usual kernel‎, ‎biased reduced kernel, and repeated biased reduced kernel methods.

Keywords

Main Subjects

References

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Journal of Statistical Modelling: Theory and Applications
Volume 6, Issue 2
July 2025
Pages 1-24

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History

  • Receive Date: 03 February 2026
  • Revise Date: 16 March 2026
  • Accept Date: 18 April 2026

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