Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics

By Hao Zhang. 2004

349 citations recorded by the source corpus.

Subfields: Environmental Engineering, Mechanical Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/339b0cebee01c7aead47a0c3dd0a450dca1b4fb5

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Citations in the corpus

Maximum‐likelihood estimation for multivariate spatial linear coregionalization models (2007, background): “Zhang (2004) showed that for a univariate stationary process observed in a fixed spatial domain, not all parameters in the Matérn covariogram are consistently estimable.”
Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach (2012, background): “Note that the asymptotic behavior of spatial covariance parameter estimators can be quite different under the two frameworks (Stein 1999; Zhang 2004).”
Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets (2008, methodology): “ Zhang (2004) used the equivalence of Gaussian measures with dierent Mat´ern covari-”
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors (2014, methodology): “with different ˝parameters are mutually singular. The statistical interpretation of this is that ˝can be inferred from a single completely observed sample of x() on any ﬁnite domain, whereas cannot (Zhang, 2004). We note that this is the parameterisation used by Lindgren et al. (2011). For this prob”
Constructing Priors that Penalize the Complexity of Gaussian Random Fields (2015, background): “The Matérn covariance function leads a ridge in the likelihood for the range and the marginal variance (Warnes and Ripley 1987), and there is no consistent estimator under in-fill asymptotics for these parameters when the base space of the GRF is of dimension three or lower (Stein 1999; Zhang 2004).”
A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components (2012, background): “Zhang (2004) showed that the parameters σ 2 and α, assuming ν is known, of a univariate Matérn covariance function cannot be estimated consistently under infill asymptotics.”
Spatial sampling design under the infill asymptotic framework (2006, methodology): “By using the infill asymptotic framework, Zhang (2004) showed that none of the parameters � 2 and ’ is consistently estimable.”
Birnbaum-Saunders spatial regression models: Diagnostics and application to chemical data (2018, background): “…according to Zhang and Zimmerman (2005), the spatial dependence parameters are not consistently estimatedupon a fixed-domain asymptotic framework (Zhang, 2004; Stein, 2012), whereas upon an increasing-domain asymptotic framework, the parameters are consistently estimated and their ML estimators…”
Spatial modelling using a new class of nonstationary covariance functions (2006, methodology): “In particular, we fix σ2φ, letting the variability of the GP be determined by ρφ (see Zhang (2004) for asymptotic justification).”
Nonstationary spatial covariance functions (2005, background): “For example, even in the simple case where the random field is Gaussian with known mean, all three functions are constant and Σ = θI, then the scalar parameters c and θ cannot be consistently estimated based on observations in a bounded subset of Rp if p 4 (Zhang 2004).”