Methods of Variance Estimation for Statistical Estimators

This thesis describes and compares some of commonly used methods of variance estimation of various statistics for dependent data. In case of stationary sequences, OBS, jackknife, moving block bootstrap and plug-in estimates that use information from time series theory are implemeted. The estimators are compared according to their mean squared errors. In case of variance estimation of sample mean for finite sample size is its exact value determined by a theoretical formula. Mean squared errors of variance estimators of sample variance and sample mean are based on simulation. Methods employed in case of spatial data in Zdor Rd are represented by subsampling or generalized moving block bootstrap as well as by the estimate based on autocovariance function estimation. Theoretical asymptotical properties of different variance estimators usually require additional assumptions such as mixing conditions