Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships
Abstract
:1. Introduction
2. Selection and Estimation of Bandwidth of Spatial Varying Coefficient Model
2.1. Spatial Varying Coefficient Model
2.2. Selection of Bandwidth Matrix
3. Simulation Experiment
4. Empirical Research
4.1. Data Sources
4.2. Modelling
4.3. Results and Analysis
4.3.1. Results of Unary Bandwidth and Bandwidth Matrix
4.3.2. Results of Bandwidth Matrix and Adaptive Bandwidth Matrix
5. Summary and Prospect
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Bandwidth Type | GCV-Based | Matrix H-Based | Adaptive Matrix H-Based |
---|---|---|---|
MSE(Y) | 3.0298 | 2.3928 | 0.6633 |
MSE() | 0.0048 | 0.0136 | 0.0011 |
MSE() | 0.0105 | 0.0137 | 0.0012 |
Running time | 14.24 s | 2.38 s | 5.67 s |
Bandwidth Type | Bandwidth h | Bandwidth Matrix H |
---|---|---|
MSE(Y) | 0.074 | 0.039 |
Running time | 33.69 min | 1.32 min |
Regression Coefficients | Minimum | 1/4 Quantile | Median | 3/4 Quantile | Maximum |
---|---|---|---|---|---|
−10.5274 | −0.0085 | 0.8041 | 1.3285 | 12.5262 | |
−0.0349 | −0.0017 | 0.0003 | 0.0021 | 0.0358 | |
−0.0788 | 0.0013 | 0.0155 | 0.0566 | 0.3834 |
Regression Coefficients | Minimum | 1/4 Quantile | Median | 3/4 Quantile | Maximum |
---|---|---|---|---|---|
−5.3196 | 0.3858 | 0.8049 | 1.1690 | 6.6727 | |
−0.0207 | −0.0011 | 0.0002 | 0.0013 | 0.0196 | |
−0.0288 | −0.0008 | 0.0141 | 0.0520 | 0.2599 |
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Hu, X.; Lu, Y.; Zhang, H.; Jiang, H.; Shi, Q. Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships. Mathematics 2021, 9, 2343. https://doi.org/10.3390/math9182343
Hu X, Lu Y, Zhang H, Jiang H, Shi Q. Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships. Mathematics. 2021; 9(18):2343. https://doi.org/10.3390/math9182343
Chicago/Turabian StyleHu, Xijian, Yaori Lu, Huiguo Zhang, Haijun Jiang, and Qingdong Shi. 2021. "Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships" Mathematics 9, no. 18: 2343. https://doi.org/10.3390/math9182343
APA StyleHu, X., Lu, Y., Zhang, H., Jiang, H., & Shi, Q. (2021). Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships. Mathematics, 9(18), 2343. https://doi.org/10.3390/math9182343