Bootstrap methods applied to spatial variogram estimation and sequential sampling

The topics, estimation of spatial variogram, bootstrap method for stationary processes and sequential sampling are studied in this thesis. Condition and exact covariance formulars are derived for Matheron\u27s variogram estimators. The asymptotic properties of the least square estimator of the spatial variogram are also shown. Block bootstrap method is applied to get more efficient generalized least square estimator. Consistency and the asymptotic normality of the bootstrap based generalized least square estimators are proved. Performances of the least square estimators with finite sample are compared by simulation study which uses the random field generated by spectral method. Bias due to the repeated significance test which is an advanced version of sequential probability ratio test is estimated by bootstrap method