Spatially Varying Coefficient Models with Sign Preservation of the Coefficient Functions
Spatially Varying Coefficient Models with Sign Preservation of the Coefficient Functions
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DOI：
10.1007/s13253-021-00443-5
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发表时间：
2021-02
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影响因子：
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通讯作者：
Myungjin Kim;Li Wang;Yu-ying Zhou
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文献类型：
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作者：
Myungjin Kim;Li Wang;Yu-ying Zhou
本文考虑了在保持系数函数符号不变的情况下，空间变系数模型的估计和推断问题。在实践中，存在各种情况，其中系数函数被假定在某个子空间中。例如，它们在域上的性质应该是非负的或非正的。然而，在系数函数的全局空间上进行优化并不能确保估计在符号中保留有意义的特征。本文在系数函数的光滑性条件下，利用新的二元样条估计，给出了系数函数的保号有效估计。我们的算法基于乘子的交替方向法，产生非负或非正的、一致和有效的估计系数函数。在系数函数具有符号约束的特定情况下，仿真研究了符号保留方法的优势。此外，在调整惩罚平滑样条法的固有偏差后，我们提出了基于剩余Bootstrap的感兴趣区域上的保号系数函数的置信度区间。最后，我们以美国的气温、地表温度和海拔为例，对我们的方法进行了评估。
This paper considers the estimation and inference of spatially varying coefficient models, while preserving the sign of the coefficient functions. In practice, there are various situations where coefficient functions are assumed to be in a certain subspace. For example, they should be either nonnegative or nonpositive on a domain by their nature. However, optimization on a global space of coefficient functions does not ensure that estimates preserve meaningful features in their signs. In this paper, we propose sign-preserved and efficient estimators of the coefficient functions using novel bivariate spline estimators under their smoothness conditions. Our algorithm, based on the alternating direction method of multipliers, yields estimated coefficient functions that are nonnegative or nonpositive, consistent, and efficient. Simulation studies are conducted to address the advantages of the sign preservation method for a specific situation, where coefficient functions have sign constraints. Furthermore, we propose residual bootstrap-based confidence intervals for sign preserving coefficient functions over the domain of interest after adjusting the inherent bias of penalized smoothing spline techniques. Finally, we evaluate our method in a case study using air temperature, land surface temperature, and elevation in the USA.Supplementary materials accompanying this paper appear online.