ON FIXED-DOMAIN ASYMPTOTICS, PARAMETER ESTIMATION AND ISOTROPIC GAUSSIAN RANDOM FIELDS WITH MATERN COVARIANCE FUNCTIONS

A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on R-d with isotropic Matern 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.

Automated summary

This study proposes a method for estimating microergodic parameters of stationary Gaussian random fields with isotropic Matern covariance functions using irregularly spaced data. The method utilizes higher-order quadratic variations and is applied to three designs, with constructed estimators shown to be consistent under mild conditions in fixed-domain asymptotics. Upper bounds to the convergence rate of the estimators are also established, and a simulation study is conducted to assess the accuracy of the proposed estimators.