Representative Points from a Mixture of Two Normal Distributions

Yinan Li, Kai-Tai Fang, Ping He () and Heng Peng
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Yinan Li: Department of Statistics and Data Science, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519087, China
Kai-Tai Fang: Department of Statistics and Data Science, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519087, China
Ping He: Department of Statistics and Data Science, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519087, China
Heng Peng: Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong

Mathematics, 2022, vol. 10, issue 21, 1-28

Abstract: 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.

Keywords: Fang-He algorithm; Kernel density estimations; k-means algorithm; mixture of normal distributions; representative points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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