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Abstract:
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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 non-negative or non-positive 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. 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 non-negative or non-positive, consistent, and efficient. 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. We evaluate our method in a case study using air temperature, land surface temperature, and elevation in the US.
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