An asymptotically unbiased weighted least squares estimation criterion for parametric variograms of second order stationary geostatistical processes

In many fields of science dealing with geostatistical data, the weighted least squares proposed by Cressie Cressie (1985 Cressie, N. 1985. Fitting variogram models by weighted least squares (1985) remains a popular choice for variogram estimation. Simplicity, ease of implementation and non-parametric nature are its principle advantages. It also avoids the heavy computational burden of Generalized least squares. But that comes at the cost of loss of information due to the use of a diagonal weight matrix. Besides, the parameter dependent weight matrix makes the estimating equations biased. In this paper we propose two alternative weight matrices which do not depend on the parameters. We show that one of the weight matrices gives parameter estimates with lower asymptotic variance and also has asymptotically unbiased estimating equations. The observations are validated using simulation and real data