Improved the bias in kernel quantile function estimation

Abdallah Sayah; Nassima Almi; Abdallah Sayah; Nassima Almi

doi:10.3934/math.2023092

AIMS Mathematics

2023, Volume 8, Issue 1: 1784-1799. doi: 10.3934/math.2023092

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Research article

Improved the bias in kernel quantile function estimation

Abdallah Sayah ^,,
Nassima Almi

Department of Mathematics and Informatic, Mohamed Khider University, Biskra, Algeria

Received: 11 July 2022 Revised: 19 September 2022 Accepted: 28 September 2022 Published: 24 October 2022
MSC : 62G05, 62G20

In this paper, a new estimator for kernel quantile estimation is given to reduce the bias. The asymptotic properties of the proposed estimator was established and it turned out that the bias has been reduced to the fourth power of the bandwidth, while the bias of the estimators considered has the second power of the bandwidth, while the variance remains at the same order. Futhermore, we calculate the optimal bandwidth which minimizes the asymptotic mean squared error. A simulation study and a real data example are carried out to illustrate the performance of the proposed estimator and compared with other existing approaches mentioned.
- bias reduction,
- quantile function,
- kernel estimation,
- order statistics,
- bandwidth
Citation: Abdallah Sayah, Nassima Almi. Improved the bias in kernel quantile function estimation[J]. AIMS Mathematics, 2023, 8(1): 1784-1799. doi: 10.3934/math.2023092

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Abstract

In this paper, a new estimator for kernel quantile estimation is given to reduce the bias. The asymptotic properties of the proposed estimator was established and it turned out that the bias has been reduced to the fourth power of the bandwidth, while the bias of the estimators considered has the second power of the bandwidth, while the variance remains at the same order. Futhermore, we calculate the optimal bandwidth which minimizes the asymptotic mean squared error. A simulation study and a real data example are carried out to illustrate the performance of the proposed estimator and compared with other existing approaches mentioned.

References

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