Kernel method for estimating overlapping coefficient using numerical integration methods. (English) Zbl 07764046
Summary: In this paper, we proposed three nonparametric kernel estimators for the overlapping Weitzman measure \(\Delta\). Due to the difficulty of finding a general expression for \(\Delta\) when the nonparametric kernel method is adopted, we suggest using the numerical integration method as the first stage of our estimation process. In particular, three numerical integration rules are considered, which are known as, trapezoidal and Simpson rules. The statistical properties of the resulting estimators are studied and investigated by using the simulation technique and their performances are also compared with some existing nonparametric kernel estimators developed by O. M. Eidous and S. A. D. A. AL-Talafha [Commun. Stat., Simulation Comput. 51, No. 9, 5139–5156 (2022; Zbl 07603807)]. The numerical results demonstrated the superiority and usefulness of the proposed technique over that suggested by Eidous and Al-Talafhah in estimating the overlapping measure \(\Delta \).
Keywords:
Weitzman measure \(\Delta\); kernel density estimation; reflection kernel; trapezoidal rule; Simpson rule; bias and relative root mean square errorCitations:
Zbl 07603807References:
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