期刊
MATHEMATICS
卷 10, 期 21, 页码 -出版社
MDPI
DOI: 10.3390/math10213952
关键词
Fang-He algorithm; Kernel density estimations; k-means algorithm; mixture of normal distributions; representative points
类别
资金
- Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science
- BNU-HKBU United International College [2022B1212010006, R202010]
This paper investigates the problem of discretizing a MixN using minimum mean squared error and provides an effective computational procedure. The study compares the proposed procedure with the k-means algorithm, demonstrating potential advantages of MSE-RPs in statistical inference.
In recent years, the mixture of two-component normal distributions (MixN) has attracted considerable interest due to its flexibility in capturing a variety of density shapes. In this paper, we investigate the problem of discretizing a MixN by a fixed number of points under the minimum mean squared error (MSE-RPs). Motivated by the Fang-He algorithm, we provide an effective computational procedure with high precision for generating numerical approximations of MSE-RPs from a MixN. We have explored the properties of the nonlinear system used to generate MSE-RPs and demonstrated the convergence of the procedure. In numerical studies, the proposed computation procedure is compared with the k-means algorithm. From an application perspective, MSE-RPs have potential advantages in statistical inference.Our numerical studies show that MSE-RPs can significantly improve Kernel density estimation.
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