Information Detection on the Spatial Varying Model

空間變異性模型訊息的探測

林子祥(Tzyy-Shyang Lin)；吳韋瑩(Wei-Ying Wu)

varying coefficient models ； B-spline ； weighted group Lasso ； fixed rank kriging ； 空間變異係數模型 ； 非參數估計 ； 懲罰函數 ； 空間相關性

中國統計學報

60卷4期（2022 / 12 / 01）

233 - 260

英文

In the traditional geostatistical model, the effect of covariates are usually assumed to be constants. However, this assumption sometimes restricts the real application. In this work, we mainly focus on the spatial varying coefficient model (SVCM), which agrees that the effect of the covariates can vary as the observation locations. Compared with the conventional stationary model, a more general mean structure in the concerned model is considered. To estimate the related model information, the non-parametric approaches with the penalty scheme is developed. The proposed approach is verified through the simulation studies.

在傳統的地質統計模型中，通常假設變量的影響係數為常數。然而，這種假設有時會限制真實的應用性。在這項工作中，我們主要關注空間變異係數模型（SVCM）。此模型允許變量的影響係數可以隨著觀察地點而變化。為了估計模型的相關信息，非參數估計方法與懲罰機制將被引入。所提出的方法之有效性將通過模擬進行驗證。

1. Ahmad, I.,Leelahanon, S.,Li, Q.(2005).Efficient estimation of a semiparametric partially linear varying coefficient model.The Annals of Statistics,33(1),258-283.
2. Brunsdon, C.,Fotheringham, A. S.,Charlton, M. E.(1998).Geographically weighted regression.Journal of the Royal Statistical Society: Series D (The Statistician),47(3),431-443.
3. Brunsdon, C.,Fotheringham, A. S.,Charlton, M. E.(1996).Geographically weighted regression: A method for exploring spatial nonstationarity.Geographical Analysis,28(4),281-298.
4. Fan, J.,Huang, T.(2005).Profile likelihood inferences on semiparametric varying-coefficient partially linear models.Bernoulli,11(6),1031-1057.
5. Fotheringham, A. S.,Brunsdon, C.,Charlton, M. E.(2002).Geographically Weighted Regression: The Analysis of Spatially Varying Relationships.John Wiley & Sons.
6. Gelfand, A. E.,Kim, H.-J.,Sirmans, C. F.,Banerjee, S.(2003).Spatial modeling with spatially varying coefficient processes.Journal of the American Statistical Association,98(462),387-396.
7. Gu, L.,Wang, L.,Härdle, W. K. K.,Yang, L.(2014).A simultaneous confidence corridor for varying coefficient regression with sparse functional data.Test,23(4),806-843.
8. Hastie, T.,Tibshirani, R.(1993).Varying-coefficient models.Journal of the Royal Statistical Society: Series B (Statistical Methodology),55(4),757-796.
9. Honda, T.,Ing, C.-K.,Wu, W.-Y.(2019).Adaptively weighted group lasso for semiparametric quantile regression models.Bernoulli,25(4B),3311-3338.
10. Huang, J. Z.,Wu, C. O.,Zhou, L.(2004).Polynomial spline estimation and inference for varying coefficient models with longitudinal data.Statistica Sinica,14(3),763-788.
11. Jiang, Q.,Wang H.,Xia, Y.,Jiang, G.(2013).On a principal varying coefficient model.Journal of the American Statistical Association,108(501),228-236.
12. Lai, M. J.,Schumaker, L. L.(2007).Spline functions on triangulations.Cambridge University Press.
13. Lai, M. J.,Wang, L.(2013).Bivariate penalized splines for regression.Statistica Sinica,23(3),1399-1417.
14. Li, X.,Wang, L.,Wang, H. J.(2021).Sparse learning and structure identification for ultra-high-dimensional image-on-scalar regression.Journal of the American Statistical Association,116(536),1994-2008.
15. Liu, J.,Li, R.,Wu, R.(2014).Feature selection for varying coefficient models with ultrahigh-dimensional covariates.Journal of the American Statistical Association,109(505),266-274.
16. Lu, Z.,Tjøstheim, D.,Yao, Q.(2009).Adaptively varying-coefficient spatiotemporal models.Journal of the Royal Statistical Society: Series B,71(4),859-880.
17. Mu, J.,Wang, G.,Wang, L.(2018).Estimation and inference in spatially varying coefficient models.Environmetrics,29(1),e2485.
18. Schumaker, L.(2007).Spline Functions: Basic Theory.Cambridge University Press.
19. Shen, S. L.,Mei, C. L.,Zhang, Y. J.(2011).Spatially varying coefficient models: Testing for spatial heteroscedasticity and reweighting estimation of the coefficients.Environment and Planning A,43(7),1723-1745.
20. Tang, Y.,Wang, H.-J.,Zhu, Z.,Song, X.(2012).A unified variable selection approach for varying coefficient models.Statistica Sinica,22(2),601-628.
21. Tzeng, S.,Huang, H.(2018).Resolution adaptive fixed rank kriging.Technometrics,60(2),198-208.
22. Wang, H. J.,Zhu, Z.,Zhou, J.(2009).Quantile regression in partially linear varying coefficient models.The Annals of Statistics,37(6B),3841-3866.
23. Zhu, H.,Fan, J.,Kong, L.(2014).Spatially varying coefficient model for neuroimaging data with jump discontinuities.Journal of the American Statistical Association,109(507),1084-1098.