Estimation of partially linear single-index spatial autoregressive model using B-splines

Lei Liu; Jun Dai; Lei Liu; Jun Dai

doi:10.3934/era.2024319

Electronic Research Archive

2024, Volume 32, Issue 12: 6822-6846. doi: 10.3934/era.2024319

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Research article

Estimation of partially linear single-index spatial autoregressive model using B-splines

Lei Liu ^{1
,
,},
Jun Dai ²

1.
Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China
2.
School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China

Received: 07 September 2024 Revised: 10 December 2024 Accepted: 18 December 2024 Published: 26 December 2024

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.
- spatial autoregressive model,
- partially linear single-index,
- B-splines
Citation: Lei Liu, Jun Dai. Estimation of partially linear single-index spatial autoregressive model using B-splines[J]. Electronic Research Archive, 2024, 32(12): 6822-6846. doi: 10.3934/era.2024319

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Abstract

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.

References

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