Bootstrap & Finite Population Complex Sampling

Since being first introduced by Efron in 1979, the
Bootstrap has quickly become one of the most largely studied, developed and applied resampling method. As a consequence of its simplicity and generality there has been much theoretical and empirical research and the bootstrap is nowadays a well established computer intensive method for assessing the precision of an estimator, confidence intervals and p-values. In its
original version the bootstrap applies in the classical non-parametric inferential context, under the customary assumption of independency and identical distribution (iid) of the sample observations from an unknown probability model. Non-iid situation are also of interest in statistical theory and practice and suitable
modifications of the original bootstrap able to address a weaker or stronger dependency structure in sample data are needed. In the seminar first the development of bootstrap method is briefly reviewed and then the non-iid finite population case is focused. Main proposals of bootstrap algorithms for complex sample are discussed and
some new results for probability proportional to size sampling are presented. Open issues and development challenges are also enlightened.