A fast, near efficient, randomized-trace based method for fitting stationary Gaussian spatial models to large noisy data sets in the case of a single range-parameter

Didier A. Girard (1)

1 IPS - Inférence Processus Stochastiques

We consider the inference problem of fitting to noisy (gridded) observations, an isotropic zero-mean stationary Gaussian field model which belongs to the Matern family with known regularity index $\nu \geq 0$, or to the spherical family. For estimating the correlation range and the variance of the field, two simple estimating functions based on the so-called ''conditional Gibbs energy mean'' (CGEM) and the empirical variance (EV) were recently introduced. This article presents a rather extensive Monte Carlo simulation study for problems with around a thousand observations and settings including large, moderate, and even ''small'', correlation ranges. It empirically demonstrates that the statistical efficiency of CGEM-EV is quite satisfying provided the signal-to-noise ratio is strong enough or $\nu$ is not too large.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Didier A. Girard. A fast, near efficient, randomized-trace based method for fitting stationary Gaussian spatial models to large noisy data sets in the case of a single range-parameter. 2010. ⟨hal-00515832v2⟩