In recent decades, functional data have become a commonly encountered type of data. Its ideal units of observation are functions defined on some continuous domain and the observed data are sampled on a discrete grid. An important problem in functional data analysis is how to fit regression models with scalar responses and functional predictors (scalar-on-function regression). This paper focuses on the nonparametric approaches to this problem. First there is a review of the classical k-nearest neighbors (kNN) method for functional regression. Then the mutual nearest neighbors (MNN) method, which is a variant of kNN method, is applied to functional regression. Compared with the classical kNN approach, the MNN method takes use of the concept of mutual nearest neighbors to construct regression model and the pseudo nearest neighbors will not be taken into account during the prediction process. In addition, any nonparametric method in the functional data cases is affected by the curse of infinite dimensionality. To prevent this curse, it is legitimate to measure the proximity between two curves via a semi-metric. The effectiveness of MNN method is illustrated by comparing the predictive power of MNN method with kNN method first on the simulated datasets and then on a real chemometrical example. The comparative experimental analyses show that MNN method preserves the main merits inherent in kNN method and achieves better performances with proper proximity measures.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 6, Issue 3) |
| DOI | 10.11648/j.sjams.20180603.13 |
| Page(s) | 81-89 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2018. Published by Science Publishing Group |
Functional Data, Nonparametric Estimation, Mutual Nearest Neighbors Estimator, Semi-Metric
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APA Style
Xingyu Chen, Dirong Chen. (2018). The Mutual Nearest Neighbor Method in Functional Nonparametric Regression. Science Journal of Applied Mathematics and Statistics, 6(3), 81-89. https://doi.org/10.11648/j.sjams.20180603.13
ACS Style
Xingyu Chen; Dirong Chen. The Mutual Nearest Neighbor Method in Functional Nonparametric Regression. Sci. J. Appl. Math. Stat. 2018, 6(3), 81-89. doi: 10.11648/j.sjams.20180603.13
AMA Style
Xingyu Chen, Dirong Chen. The Mutual Nearest Neighbor Method in Functional Nonparametric Regression. Sci J Appl Math Stat. 2018;6(3):81-89. doi: 10.11648/j.sjams.20180603.13
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Download@article{10.11648/j.sjams.20180603.13,
author = {Xingyu Chen and Dirong Chen},
title = {The Mutual Nearest Neighbor Method in Functional Nonparametric Regression},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {6},
number = {3},
pages = {81-89},
doi = {10.11648/j.sjams.20180603.13},
url = {https://doi.org/10.11648/j.sjams.20180603.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20180603.13},
abstract = {In recent decades, functional data have become a commonly encountered type of data. Its ideal units of observation are functions defined on some continuous domain and the observed data are sampled on a discrete grid. An important problem in functional data analysis is how to fit regression models with scalar responses and functional predictors (scalar-on-function regression). This paper focuses on the nonparametric approaches to this problem. First there is a review of the classical k-nearest neighbors (kNN) method for functional regression. Then the mutual nearest neighbors (MNN) method, which is a variant of kNN method, is applied to functional regression. Compared with the classical kNN approach, the MNN method takes use of the concept of mutual nearest neighbors to construct regression model and the pseudo nearest neighbors will not be taken into account during the prediction process. In addition, any nonparametric method in the functional data cases is affected by the curse of infinite dimensionality. To prevent this curse, it is legitimate to measure the proximity between two curves via a semi-metric. The effectiveness of MNN method is illustrated by comparing the predictive power of MNN method with kNN method first on the simulated datasets and then on a real chemometrical example. The comparative experimental analyses show that MNN method preserves the main merits inherent in kNN method and achieves better performances with proper proximity measures.},
year = {2018}
}
TY - JOUR T1 - The Mutual Nearest Neighbor Method in Functional Nonparametric Regression AU - Xingyu Chen AU - Dirong Chen Y1 - 2018/07/19 PY - 2018 N1 - https://doi.org/10.11648/j.sjams.20180603.13 DO - 10.11648/j.sjams.20180603.13 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 81 EP - 89 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20180603.13 AB - In recent decades, functional data have become a commonly encountered type of data. Its ideal units of observation are functions defined on some continuous domain and the observed data are sampled on a discrete grid. An important problem in functional data analysis is how to fit regression models with scalar responses and functional predictors (scalar-on-function regression). This paper focuses on the nonparametric approaches to this problem. First there is a review of the classical k-nearest neighbors (kNN) method for functional regression. Then the mutual nearest neighbors (MNN) method, which is a variant of kNN method, is applied to functional regression. Compared with the classical kNN approach, the MNN method takes use of the concept of mutual nearest neighbors to construct regression model and the pseudo nearest neighbors will not be taken into account during the prediction process. In addition, any nonparametric method in the functional data cases is affected by the curse of infinite dimensionality. To prevent this curse, it is legitimate to measure the proximity between two curves via a semi-metric. The effectiveness of MNN method is illustrated by comparing the predictive power of MNN method with kNN method first on the simulated datasets and then on a real chemometrical example. The comparative experimental analyses show that MNN method preserves the main merits inherent in kNN method and achieves better performances with proper proximity measures. VL - 6 IS - 3 ER -
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