In this article, we consider the problem of modeling nonstationary spatial random processes. Bornn et al.(2012) proposed a dimension expansion method, a novel technique for modeling nonstationary processes, aiming to find a dimensionally sparse projection in which the originally nonstationary field exhibits stationarity. However, their dimension expansion approach is a lasso-penalized least-squares method that does not account for the covariance structure of the empirical semivariogram. We thus propose a general latent dimension estimation method by replacing the least-squares method with generalized least-squares (GLS). Furthermore, we improve the GLS method by weighted least-squares, which is more computationally efficient and accurate. The performance of the proposed methods is demonstrated through simulations and real data examples.

中文翻译：

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非平稳过程维数扩展方法中的广义最小二乘法

在本文中，我们考虑对非平稳空间随机过程进行建模的问题。Bornn et al.(2012) 提出了一种维数扩展方法，一种对非平稳过程建模的新技术，旨在找到一个维度稀疏的投影，其中原始非平稳场表现出平稳性。然而，他们的维度扩展方法是一种套索惩罚最小二乘法，不考虑经验半变异函数的协方差结构。因此，我们通过用广义最小二乘法 (GLS) 替换最小二乘法方法，提出了一种通用的潜在维数估计方法。此外，我们通过加权最小二乘法改进了 GLS 方法，这在计算上更加高效和准确。通过模拟和实际数据示例证明了所提出方法的性能。