A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics

8 Efron (1979) introduced the bootstrap method for independent data but it can not be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is related to the block size which is difficult to select. In the moving block bootstrap method also the variance estimator is underestimated. In this paper, first the semi-parametric bootstrap is used to estimate the precision measures of estimators in spatial data analysis. In the semiparametric bootstrap method, we use the estimation of spatial correlation structure. Then, we compare the semi-parametric bootstrap with a moving block bootstrap for variance estimation of estimators in a simulation study. ∗Corresponding author. Tel. and fax: +98 21 82883483; Email address: mohsen [email protected] (M. Mohammadzadeh) Preprint submitted to Computational Statistics and Data Analysis October 31, 2012 Finally, we use the semi-parametric bootstrap to analyze the coal-ash data.