文章基本信息

标题：Local inversion-free estimation of spatial Gaussian processes
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作者：Hossein Keshavarz ; XuanLong Nguyen ; Clayton Scott 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：4224-4279
DOI：10.1214/19-EJS1592
语种：English
出版社：Institute of Mathematical Statistics
摘要：Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for large number of (possibly) irregularly spaced observations, due to the need to handle the inverse of ill-conditioned and large covariance matrices. Extending the “inversion-free” method of Anitescu, Chen and Stein [1], we investigate a broad class of covariance parameter estimation based on inversion-free surrogate losses and block diagonal approximation schemes of the covariance structure. This class of estimators yields a spectrum for negotiating the trade-off between statistical accuracy and computational cost. We present fixed-domain asymptotic properties of our proposed method, establishing $\sqrt{n}$-consistency and asymptotic normality results for isotropic Matern Gaussian processes observed on a multi-dimensional and irregular lattice. Simulation studies are also presented for assessing the scalability and statistical efficiency of the proposed algorithm for large data sets.
关键词：Local inversion-free covariance estimation; Gaussian process; computationally scalable; fixed-domain asymptotic analysis; irregularly spaced observations