On fixed-domain asymptotics, parameter estimation and isotropic Gaussian random fields with Matérn covariance functions
提出一种利用不规则空间数据估计各向同性Matérn协方差函数中微遍历参数（包括平滑参数）的方法，基于高阶二次变差，在三种采样设计下证明估计量的一致性并给出收敛速度上界，模拟验证了准确性。
A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on Rd with isotropic Matérn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under mild conditions, these estimators are shown to be consistent with respect to fixed-domain asymptotics. Upper bounds to the convergence rate of the estimators are also established. A simulation study is conducted to gauge the accuracy of the proposed estimators.