Separate Block Bootstrap Method for Determining the Precision Measures of the Variogram Parameters Estimator and Spatial Prediction

In many environmental studies, the collected data are usually spatially dependent. Determination of the spatial correlation structure of the data and prediction are two important problem in statistical analysis of spatial data. To do so, often, a parametric variogram model is fitted to the empirical variogram of the data by estimating the unknown parameters of the mentioned variogram. Since there are no closed formulas for the variogram parameters estimator, they are usually computed numerically. Therefore, the precision measures of the variogram parameters estimator and spatial prediction can be calculated using bootstrap methods. Lahiri (2003) proposed the moving block bootstrap method for spatial data, in which observations are divided into several moving blocks and resampling is done from them. Since, in this method, the presence of boundary observations in the resampling blocks have less selection chance than the other observations, therefore, the estimator of the precision measures would be biased. In this paper, revising the moving block bootstrap method, the separate block bootstrap method was presented for estimating the precision measures of the variogram parameters estimator and spatial prediction. Then its usage was illustrated in an applied example.