Two generalized bootstrap methods with check- and quantile-based filtering to estimate parameter uncertainty for exponential semi-variogram models

Abstract Estimation of parameter standard errors for semi-variogram models is challenging, given the two-step process required to fit a parametric model to spatially correlated data. Motivated by an application in social epidemiology, we focus on exponential semi-variogram models fitted to data with 500 to 2000 observations and little control over the sampling design. Previously proposed methods for the estimation of standard errors cannot be applied in this context. Approximate closed form solutions are too costly using generalized least squares in terms of memory capacities. The generalized bootstrap proposed by Olea and Pardo-Igúzquiza is nonetheless applicable with weighted instead of generalized least squares. However, the standard error estimates are hugely biased and imprecise. Therefore, we propose to add a filter mechanism to the generalized bootstrap. The new development is presented and evaluated with a simulation study which shows that the generalized bootstrap with check-based filtering leads to massively improved results compared to the generalized bootstrap method without filtering. We provide a case study using birthweight data.