INFILL ASYMPTOTICS FOR A STOCHASTIC PROCESS MODEL WITH MEASUREMENT ERROR

By Huann-Sheng Chen, D. Simpson, Zhiliang Ying. 2000

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A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data (2013, background): “For example, the maximum likelihood estimator is consistent and asymptotically normally distributed for many covariance models under expanding-domain asymptotics (Mardia and Marchall 1984), whereas such consistent estimators do not exist under infill asymptotics (Chen et al. 2000).”
Spatial designs and properties of spatial correlation: Effects on covariance estimation (2007, background): “separately can be consistently estimated (again, under in-fill asymptotics) (Chen et al. 2000; Zhang and Zimmerman 2005).”
Spatial sampling design for parameter estimation of the covariance function (2005, background): “Chen et al. (2000) derived results for exponential correlation functions with nugget effect.”
The role of the range parameter for estimation and prediction in geostatistics (2011, background): “However, in a restricted version of thisproblem, the introduction of the error term reduces the rate of convergence of the maxi um likelihood estimator forc from the usual ordern−1/2 to ordern−1/4 (Chen et al., 2000).”