Detection of Interaction Effects in a Nonparametric Concurrent Regression Model
Many methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study interaction effects among these functional covariat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/9/1327 |
| _version_ | 1797580135882293248 |
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| author | Rui Pan Zhanfeng Wang Yaohua Wu |
| author_facet | Rui Pan Zhanfeng Wang Yaohua Wu |
| author_sort | Rui Pan |
| collection | DOAJ |
| description | Many methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study interaction effects among these functional covariates, in this article, we first construct a tensor product space of reproducing kernel Hilbert spaces and build an analysis of variance (ANOVA) decomposition of the tensor product space. We then use a model selection method with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>1</mn></msub></semantics></math></inline-formula> criterion to estimate the functional function with functional covariate inputs and detect interaction effects among the functional covariates. The proposed method is evaluated using simulations and stroke rehabilitation data. |
| first_indexed | 2024-03-10T22:47:01Z |
| format | Article |
| id | doaj.art-269ab1cb7179489db284683f022fc65a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T22:47:01Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-269ab1cb7179489db284683f022fc65a2023-11-19T10:36:04ZengMDPI AGEntropy1099-43002023-09-01259132710.3390/e25091327Detection of Interaction Effects in a Nonparametric Concurrent Regression ModelRui Pan0Zhanfeng Wang1Yaohua Wu2School of Data Science, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Statistics and Finance, Management School, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Statistics and Finance, Management School, University of Science and Technology of China, Hefei 230026, ChinaMany methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study interaction effects among these functional covariates, in this article, we first construct a tensor product space of reproducing kernel Hilbert spaces and build an analysis of variance (ANOVA) decomposition of the tensor product space. We then use a model selection method with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>1</mn></msub></semantics></math></inline-formula> criterion to estimate the functional function with functional covariate inputs and detect interaction effects among the functional covariates. The proposed method is evaluated using simulations and stroke rehabilitation data.https://www.mdpi.com/1099-4300/25/9/1327model selection<i>L</i><sub>1</sub> criterionreproducing kernel Hilbert spacesmoothing spline |
| spellingShingle | Rui Pan Zhanfeng Wang Yaohua Wu Detection of Interaction Effects in a Nonparametric Concurrent Regression Model Entropy model selection <i>L</i><sub>1</sub> criterion reproducing kernel Hilbert space smoothing spline |
| title | Detection of Interaction Effects in a Nonparametric Concurrent Regression Model |
| title_full | Detection of Interaction Effects in a Nonparametric Concurrent Regression Model |
| title_fullStr | Detection of Interaction Effects in a Nonparametric Concurrent Regression Model |
| title_full_unstemmed | Detection of Interaction Effects in a Nonparametric Concurrent Regression Model |
| title_short | Detection of Interaction Effects in a Nonparametric Concurrent Regression Model |
| title_sort | detection of interaction effects in a nonparametric concurrent regression model |
| topic | model selection <i>L</i><sub>1</sub> criterion reproducing kernel Hilbert space smoothing spline |
| url | https://www.mdpi.com/1099-4300/25/9/1327 |
| work_keys_str_mv | AT ruipan detectionofinteractioneffectsinanonparametricconcurrentregressionmodel AT zhanfengwang detectionofinteractioneffectsinanonparametricconcurrentregressionmodel AT yaohuawu detectionofinteractioneffectsinanonparametricconcurrentregressionmodel |