On fixed-domain asymptotics, parameter estimation and isotropic Gaussian random fields with Matérn covariance functions
固定域渐近下具有 Matérn 协方差的各向同性高斯随机场参数估计
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…