The role of the range parameter for estimation and prediction in geostatistics

By Cari Kaufman, B. Shaby. 2011

117 citations recorded by the source corpus.

Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. We show that asymptotic results for a Gaussian process over a fixed domain with Matern covariance function, previously proven only in the case of a fixed range parameter, can be extended to the case of jointly estimating the range and the variance of the process. Moreover, we show that intuition and approximations derived from asymptotics using a fixed range parameter can be problematic when applied to finite samples, even for large sample sizes. In contrast, we show via simulation that performance is improved and asymptotic approximations are applicable for smaller sample sizes when the parameters are jointly estimated. These effects are particularly apparent when the process is mean square differentiable or the effective range of spatial correlation is small. Copyright 2013, Oxford University Press.

Subfields: Environmental Engineering, Mechanical Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/03de707a2c4bd02e8ad6f420a4ecf699bcddb20d

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Citations in the corpus

The Prior Can Often Only Be Understood in the Context of the Likelihood (2017, background): “While it may be tempting to resolve this non-identifiability by fixing κ, there is strong empirical (Kaufman and Shaby, 2013) and theoretical (van der Vaart and van Zanten, 2009) evidence that the models will fit the data better if the parameter is allowed to vary.”
Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics (2016, methodology): “The proof follows the lines of Kaufman and Shaby (2013), and we omit it. As outlined in Kaufman and Shaby (2013), we also conjecture that (28) and (29) hold if β1 is replaced by its maximum likelihood estimator.”
Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field (2014, background): “Further, for spatial Gaussian models with known mean and a stationary Matérn covariance function, it has been shown that for a fixed domain and in-fill asymptotics there are no consistent estimators for all covariance parameters (Zhang, 2004; Kaufman and Shaby, 2013), i.”