K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples
Functional data, which provides information about curves, surfaces or anything else varying over a continuum, has become a commonly encountered type of data. The k-nearest neighbor (kNN) method, as a nonparametric method, has become one of the most popular supervised machine learning algorithms used...
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| Format: | Article |
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MDPI AG
2022-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/3/102 |
| _version_ | 1797447207879704576 |
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| author | Xueping Hu Jingya Wang Liuliu Wang Keming Yu |
| author_facet | Xueping Hu Jingya Wang Liuliu Wang Keming Yu |
| author_sort | Xueping Hu |
| collection | DOAJ |
| description | Functional data, which provides information about curves, surfaces or anything else varying over a continuum, has become a commonly encountered type of data. The k-nearest neighbor (kNN) method, as a nonparametric method, has become one of the most popular supervised machine learning algorithms used to solve both classification and regression problems. This paper is devoted to the k-nearest neighbor (kNN) estimators of the nonparametric functional regression model when the observed variables take values from negatively associated (NA) sequences. The consistent and complete convergence rate for the proposed kNN estimator is first provided. Then, numerical assessments, including simulation study and real data analysis, are conducted to evaluate the performance of the proposed method and compare it with the standard nonparametric kernel approach. |
| first_indexed | 2024-03-09T13:51:35Z |
| format | Article |
| id | doaj.art-e59ab1480b9b4f49931b80adb5f91967 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:51:35Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-e59ab1480b9b4f49931b80adb5f919672023-11-30T20:49:55ZengMDPI AGAxioms2075-16802022-02-0111310210.3390/axioms11030102K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA SamplesXueping Hu0Jingya Wang1Liuliu Wang2Keming Yu3College of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaCollege of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaCollege of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaCollege of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaFunctional data, which provides information about curves, surfaces or anything else varying over a continuum, has become a commonly encountered type of data. The k-nearest neighbor (kNN) method, as a nonparametric method, has become one of the most popular supervised machine learning algorithms used to solve both classification and regression problems. This paper is devoted to the k-nearest neighbor (kNN) estimators of the nonparametric functional regression model when the observed variables take values from negatively associated (NA) sequences. The consistent and complete convergence rate for the proposed kNN estimator is first provided. Then, numerical assessments, including simulation study and real data analysis, are conducted to evaluate the performance of the proposed method and compare it with the standard nonparametric kernel approach.https://www.mdpi.com/2075-1680/11/3/102convergence rateNA samplesfunctional datanonparametric regression modelk-nearest neighbor estimator |
| spellingShingle | Xueping Hu Jingya Wang Liuliu Wang Keming Yu K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples Axioms convergence rate NA samples functional data nonparametric regression model k-nearest neighbor estimator |
| title | K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples |
| title_full | K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples |
| title_fullStr | K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples |
| title_full_unstemmed | K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples |
| title_short | K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples |
| title_sort | k nearest neighbor estimation of functional nonparametric regression model under na samples |
| topic | convergence rate NA samples functional data nonparametric regression model k-nearest neighbor estimator |
| url | https://www.mdpi.com/2075-1680/11/3/102 |
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