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)

《中國統計學報》 60卷4期 (2022/12) Pp. 233-260

摘要

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.

關鍵字

varying coefficient models ； B-spline ； weighted group Lasso ； fixed rank kriging

並列摘要

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。

並列關鍵字

空間變異係數模型 ； 非參數估計 ； 懲罰函數 ； 空間相關性

參考文獻

Ahmad, I., Leelahanon, S., and Li, Q. (2005). Efficient estimation of a semiparametric partially linear varying coefficient model. The Annals of Statistics, 33(1), pages 258-283.

Brunsdon, C., Fotheringham, A. S., and Charlton, M. E. (1996). Geographically weighted regression: A method for exploring spatial nonstationarity. Geographical Analysis, 28(4), pages 281-298.

Brunsdon, C., Fotheringham, A. S. and Charlton, M. E. (1998). Geographically weighted regression. Journal of the Royal Statistical Society: Series D (The Statistician), 47(3), pages 431-443.

Fan, J., and Huang, T. (2005). Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli, 11(6), pages 1031-1057.

Fotheringham, A. S., Brunsdon, C., and Charlton, M. E. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. John Wiley & Sons.