Exact Boundary Correction Methods for Multivariate Kernel Density Estimation
This paper develops a method to obtain multivariate kernel functions for density estimation problems in which the density function is defined on compact support. If domain-specific knowledge requires certain conditions to be satisfied at the boundary of the support of an unknown density, the propose...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/9/1670 |
| _version_ | 1797576627400474624 |
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| author | Ji-Yeon Yang |
| author_facet | Ji-Yeon Yang |
| author_sort | Ji-Yeon Yang |
| collection | DOAJ |
| description | This paper develops a method to obtain multivariate kernel functions for density estimation problems in which the density function is defined on compact support. If domain-specific knowledge requires certain conditions to be satisfied at the boundary of the support of an unknown density, the proposed method incorporates the information contained in the boundary conditions into the kernel density estimators. The proposed method provides an exact kernel function that satisfies the boundary conditions, even for small samples. Existing methods primarily deal with a one-sided boundary in a one-dimensional problem. We consider density in a two-sided interval and extend it to a multi-dimensional problem. |
| first_indexed | 2024-03-10T21:54:36Z |
| format | Article |
| id | doaj.art-7efd5d66655a464b8e1d4c013aad03a4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T21:54:36Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7efd5d66655a464b8e1d4c013aad03a42023-11-19T13:11:00ZengMDPI AGSymmetry2073-89942023-08-01159167010.3390/sym15091670Exact Boundary Correction Methods for Multivariate Kernel Density EstimationJi-Yeon Yang0Department of Mathematics and Big Data Science, Kumoh National Institute of Technology, 61 Daehak-Ro, Gumi 39177, Republic of KoreaThis paper develops a method to obtain multivariate kernel functions for density estimation problems in which the density function is defined on compact support. If domain-specific knowledge requires certain conditions to be satisfied at the boundary of the support of an unknown density, the proposed method incorporates the information contained in the boundary conditions into the kernel density estimators. The proposed method provides an exact kernel function that satisfies the boundary conditions, even for small samples. Existing methods primarily deal with a one-sided boundary in a one-dimensional problem. We consider density in a two-sided interval and extend it to a multi-dimensional problem.https://www.mdpi.com/2073-8994/15/9/1670kernel density estimationmultivariate density functioncompact supportboundary conditionsnonparametric estimationheat equation |
| spellingShingle | Ji-Yeon Yang Exact Boundary Correction Methods for Multivariate Kernel Density Estimation Symmetry kernel density estimation multivariate density function compact support boundary conditions nonparametric estimation heat equation |
| title | Exact Boundary Correction Methods for Multivariate Kernel Density Estimation |
| title_full | Exact Boundary Correction Methods for Multivariate Kernel Density Estimation |
| title_fullStr | Exact Boundary Correction Methods for Multivariate Kernel Density Estimation |
| title_full_unstemmed | Exact Boundary Correction Methods for Multivariate Kernel Density Estimation |
| title_short | Exact Boundary Correction Methods for Multivariate Kernel Density Estimation |
| title_sort | exact boundary correction methods for multivariate kernel density estimation |
| topic | kernel density estimation multivariate density function compact support boundary conditions nonparametric estimation heat equation |
| url | https://www.mdpi.com/2073-8994/15/9/1670 |
| work_keys_str_mv | AT jiyeonyang exactboundarycorrectionmethodsformultivariatekerneldensityestimation |