### B-Spline Method for Spatio-Temporal Inverse Model

WANG Hongxia1, ZHAO Zihan1, WU Yuehua2, LUO Xuehong3

1. 1. School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China;
2. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada;
3. Department of Statistics and Data Science, School of Economics, Xiamen University, Xiamen 361005, China
• Received:2021-06-20 Revised:2022-04-20 Online:2022-11-25 Published:2022-12-23
• Supported by:
This research was supported by the National Social Science Fund of China under Grant No. 22BTJ021, "Qinglan project" of Colleges and Universities of Jiangsu Province and Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant No. KYCX21_1941.

WANG Hongxia, ZHAO Zihan, WU Yuehua, LUO Xuehong. B-Spline Method for Spatio-Temporal Inverse Model[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2336-2360.

Inverse models can be used to estimate surface fluxes in terms of the observed atmospheric concentration measurement data. This paper proposes a new nonparametric spatio-temporal inverse model and provides the global expressions for the estimates by employing the B-spline method. The authors establish the asymptotic normality of the estimators under mild conditions. The authors also conduct numerical studies to evaluate the finite sample performance of the proposed methodologies. Finally, the authors apply the method to anthropogenic carbon dioxide (CO${}_{2}$) emission data from different provinces of Canada to illustrate the validity of the proposed techniques.
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