Estimation and Inference for Spatio-Temporal Single-Index Models
To better fit the actual data, this paper will consider both spatio-temporal correlation and heterogeneity to build the model. In order to overcome the “curse of dimensionality” problem in the nonparametric method, we improve the estimation method of the single-index model and combine it with the co...
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| Format: | Article |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4289 |
| _version_ | 1827720530891898880 |
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| author | Hongxia Wang Zihan Zhao Hongxia Hao Chao Huang |
| author_facet | Hongxia Wang Zihan Zhao Hongxia Hao Chao Huang |
| author_sort | Hongxia Wang |
| collection | DOAJ |
| description | To better fit the actual data, this paper will consider both spatio-temporal correlation and heterogeneity to build the model. In order to overcome the “curse of dimensionality” problem in the nonparametric method, we improve the estimation method of the single-index model and combine it with the correlation and heterogeneity of the spatio-temporal model to obtain a good estimation method. In this paper, assuming that the spatio-temporal process obeys the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> mixing condition, a nonparametric procedure is developed for estimating the variance function based on a fully nonparametric function or dimensional reduction structure, and the resulting estimator is consistent. Then, a reweighting estimation of the parametric component can be obtained via taking the estimated variance function into account. The rate of convergence and the asymptotic normality of the new estimators are established under mild conditions. Simulation studies are conducted to evaluate the efficacy of the proposed methodologies, and a case study about the estimation of the air quality evaluation index in Nanjing is provided for illustration. |
| first_indexed | 2024-03-10T21:04:47Z |
| format | Article |
| id | doaj.art-7cb9a4021147413683e5da87e4e3f211 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:04:47Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7cb9a4021147413683e5da87e4e3f2112023-11-19T17:13:53ZengMDPI AGMathematics2227-73902023-10-011120428910.3390/math11204289Estimation and Inference for Spatio-Temporal Single-Index ModelsHongxia Wang0Zihan Zhao1Hongxia Hao2Chao Huang3School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, ChinaSchool of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, ChinaSchool of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, ChinaDepartment of Statistics, Florida State University, Tallahassee, FL 32306, USATo better fit the actual data, this paper will consider both spatio-temporal correlation and heterogeneity to build the model. In order to overcome the “curse of dimensionality” problem in the nonparametric method, we improve the estimation method of the single-index model and combine it with the correlation and heterogeneity of the spatio-temporal model to obtain a good estimation method. In this paper, assuming that the spatio-temporal process obeys the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> mixing condition, a nonparametric procedure is developed for estimating the variance function based on a fully nonparametric function or dimensional reduction structure, and the resulting estimator is consistent. Then, a reweighting estimation of the parametric component can be obtained via taking the estimated variance function into account. The rate of convergence and the asymptotic normality of the new estimators are established under mild conditions. Simulation studies are conducted to evaluate the efficacy of the proposed methodologies, and a case study about the estimation of the air quality evaluation index in Nanjing is provided for illustration.https://www.mdpi.com/2227-7390/11/20/4289spatio-temporal correlationspatio-temporal heterogeneityreweighting estimationlocal linear methodsingle-index models |
| spellingShingle | Hongxia Wang Zihan Zhao Hongxia Hao Chao Huang Estimation and Inference for Spatio-Temporal Single-Index Models Mathematics spatio-temporal correlation spatio-temporal heterogeneity reweighting estimation local linear method single-index models |
| title | Estimation and Inference for Spatio-Temporal Single-Index Models |
| title_full | Estimation and Inference for Spatio-Temporal Single-Index Models |
| title_fullStr | Estimation and Inference for Spatio-Temporal Single-Index Models |
| title_full_unstemmed | Estimation and Inference for Spatio-Temporal Single-Index Models |
| title_short | Estimation and Inference for Spatio-Temporal Single-Index Models |
| title_sort | estimation and inference for spatio temporal single index models |
| topic | spatio-temporal correlation spatio-temporal heterogeneity reweighting estimation local linear method single-index models |
| url | https://www.mdpi.com/2227-7390/11/20/4289 |
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