This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a linear combination of the wavelet basis. The estimate of the deformation guarantees an injective transformation. Such that two distinct locations in the geographic plane are not mapped into the same point in the deformation plane. Simulation studies have shown the effectiveness of this procedure. An application to historical daily maximum temperature records exemplifies the flexibility of the proposed methodology when dealing with real datasets.

翻译：本文提出了一种用于估计时空形变中非平稳空间协方差函数的新方法。该方法基于单调函数途径，将形变函数展开为小波基函数的线性组合。所估计的形变保证了变换的单射性，确保地理平面中任意两个不同位置不会映射到形变平面中的同一个点。模拟研究验证了该方法的有效性。通过对历史日最高气温记录的应用实例，展示了所提出方法在处理真实数据集时的灵活性。