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.
Makhdoom, I. and Salehi, R. (2025). On bias reduction for probability density function estimation based on a kernel estimator. Journal of Statistical Modelling: Theory and Applications, 6(2), 1-24. doi: 10.22034/jsmta.2026.24296.1210
MLA
Makhdoom, I. , and Salehi, R. . "On bias reduction for probability density function estimation based on a kernel estimator", Journal of Statistical Modelling: Theory and Applications, 6, 2, 2025, 1-24. doi: 10.22034/jsmta.2026.24296.1210
HARVARD
Makhdoom, I., Salehi, R. (2025). 'On bias reduction for probability density function estimation based on a kernel estimator', Journal of Statistical Modelling: Theory and Applications, 6(2), pp. 1-24. doi: 10.22034/jsmta.2026.24296.1210
CHICAGO
I. Makhdoom and R. Salehi, "On bias reduction for probability density function estimation based on a kernel estimator," Journal of Statistical Modelling: Theory and Applications, 6 2 (2025): 1-24, doi: 10.22034/jsmta.2026.24296.1210
VANCOUVER
Makhdoom, I., Salehi, R. On bias reduction for probability density function estimation based on a kernel estimator. Journal of Statistical Modelling: Theory and Applications, 2025; 6(2): 1-24. doi: 10.22034/jsmta.2026.24296.1210
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