Estimation of partially linear single-index spatial autoregressive model using B-splines
Possible dependence across spatial units is a relevant issue in many areas in practice. In this paper, we consider the partially linear single-index spatial autoregressive model to analyze the dependence of the spatial units and suggest an estimation method. An algorithm procedure is proposed to est...
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AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024319 |
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| author | Lei Liu Jun Dai |
| author_facet | Lei Liu Jun Dai |
| author_sort | Lei Liu |
| collection | DOAJ |
| description | Possible dependence across spatial units is a relevant issue in many areas in practice. In this paper, we consider the partially linear single-index spatial autoregressive model to analyze the dependence of the spatial units and suggest an estimation method. An algorithm procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component and the spatial parameter of the model. The nonparametric function is estimated based on B-spline approximation. The Nelder-Mead iteration algorithm is adopted to calculate the parametric and nonparametric parts simultaneously in the optimization. The asymptotic properties of parameter and function estimates are established. Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimation methodology and calculation procedure. Furthermore, we use the proposed method to analyze air quality data and rural household income data in China. |
| format | Article |
| id | doaj-art-79a7e731c9284b228effe4df7e4f2640 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-79a7e731c9284b228effe4df7e4f26402025-01-23T07:53:06ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126822684610.3934/era.2024319Estimation of partially linear single-index spatial autoregressive model using B-splinesLei Liu0Jun Dai1Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, ChinaSchool of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, ChinaPossible dependence across spatial units is a relevant issue in many areas in practice. In this paper, we consider the partially linear single-index spatial autoregressive model to analyze the dependence of the spatial units and suggest an estimation method. An algorithm procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component and the spatial parameter of the model. The nonparametric function is estimated based on B-spline approximation. The Nelder-Mead iteration algorithm is adopted to calculate the parametric and nonparametric parts simultaneously in the optimization. The asymptotic properties of parameter and function estimates are established. Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimation methodology and calculation procedure. Furthermore, we use the proposed method to analyze air quality data and rural household income data in China.https://www.aimspress.com/article/doi/10.3934/era.2024319spatial autoregressive modelpartially linear single-indexb-splines |
| spellingShingle | Lei Liu Jun Dai Estimation of partially linear single-index spatial autoregressive model using B-splines Electronic Research Archive spatial autoregressive model partially linear single-index b-splines |
| title | Estimation of partially linear single-index spatial autoregressive model using B-splines |
| title_full | Estimation of partially linear single-index spatial autoregressive model using B-splines |
| title_fullStr | Estimation of partially linear single-index spatial autoregressive model using B-splines |
| title_full_unstemmed | Estimation of partially linear single-index spatial autoregressive model using B-splines |
| title_short | Estimation of partially linear single-index spatial autoregressive model using B-splines |
| title_sort | estimation of partially linear single index spatial autoregressive model using b splines |
| topic | spatial autoregressive model partially linear single-index b-splines |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024319 |
| work_keys_str_mv | AT leiliu estimationofpartiallylinearsingleindexspatialautoregressivemodelusingbsplines AT jundai estimationofpartiallylinearsingleindexspatialautoregressivemodelusingbsplines |