Three Alternatives to the Likelihood Maximization for Estimating a Centered Matérn (3/2) Process
Résumé
http://demonstrations.wolfram.com/ThreeAlternativesToTheLikelihoodMaximizationForEstimatingACe/.
This demonstration considers the estimation of the two parameters of a stationary Gaussian series with a Matérn-3/2 correlation. Three fast methods are compared: the classical variogram fitting, an hybrid method advocated by H. Zhang and D. L. Zimmerman in the paper "Hybrid Estimation of Semivariogram Parameters," Mathematical Geology, 2007, and the recently proposed GE-EV method [see "Asymptotic near-efficiency of the “Gibbs-energy and empirical-variance” estimating functions for fitting Matérn models — I: Densely sampled processes",
Statistics & Probability Letters, 2016].
For GE-EV, a simple fixed-point algorithm is used here: it proves to be successful with quite fast convergence.
For "small range" settings, a ranking of GE-EV and the hybrid method based on their statistical performances is rather difficult, but for "large range" settings, a clear improvement by using GE-EV in place of the hybrid method can be observed (and the variogram fitting method produces even more variable estimates).