An Improved Model for Kernel Density Estimation Based on Quadtree and Quasi-Interpolation

Jiecheng Wang, Yantong Liu and Jincai Chang
Additional contact information
Jiecheng Wang: Department of Statistics, School of Economics, Anhui University, Hefei 230039, China
Yantong Liu: School of Management, North China University of Science and Technology, Tangshan 063210, China
Jincai Chang: School of Science, North China University of Science and Technology, Tangshan 063210, China

Mathematics, 2022, vol. 10, issue 14, 1-15

Abstract: There are three main problems for classical kernel density estimation in its application: boundary problem, over-smoothing problem of high (low)-density region and low-efficiency problem of large samples. A new improved model of multivariate adaptive binned quasi-interpolation density estimation based on a quadtree algorithm and quasi-interpolation is proposed, which can avoid the deficiency in the classical kernel density estimation model and improve the precision of the model. The model is constructed in three steps. Firstly, the binned threshold is set from the three dimensions of sample number, width of bins and kurtosis, and the bounded domain is adaptively partitioned into several non-intersecting bins (intervals) by using the iteration idea from the quadtree algorithm. Then, based on the good properties of the quasi-interpolation, the kernel functions of the density estimation model are constructed by introducing the theory of quasi-interpolation. Finally, the binned coefficients of the density estimation model are constructed by using the idea of frequency replacing probability. Simulation of the Monte Carlo method shows that the proposed non-parametric model can effectively solve the three shortcomings of the classical kernel density estimation model and significantly improve the prediction accuracy and calculation efficiency of the density function for large samples.

Keywords: large samples; kernel density estimation; quasi-interpolation; quadtree algorithm; adaptive (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 (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/14/2402/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/14/2402/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:14:p:2402-:d:858749

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().