BOOTSTRAP METHODS FOR FINITE POPULATION SAMPLING

The estimation of the reliability of sample survey estimates for finite population characteristics is an important statistical problem with practical implications. The bootstrap method is a new procedure for estimating standard errors of statistics. This research examines the applicability of the bootstrap method to finite population sampling problems. The bootstrap is applied in the design based and the prediction approach to survey sampling. The research proceeds by first examining the bootstrap approximations to problems for which there are exact, theoretical results. The bootstrap is then extended to problems for which there are no exact formulae for finding the standard error of the estimate. In the design based approach the bootstrap method is used to approximate the standard error of the inflation estimator of the total and the sample median. The bootstrap estimators for the inflation estimator are nearly identical to the standard theoretical results. The bootstrap bias and standard error for the sample median are examined in a small empirical study. The bootstrap standard error appears to be a reliable approximation of the standard error of the sample median. The bootstrap method is employed for two regression models in the prediction approach. For both models the bootstrap method produces estimators of the bias and standard error of the predictors which are almost equal to known theoretical results. The bootstrap technique is also applied to the problem of predicting the population median using the sample median in a given model. No closed form solution is found but simulation can be used to obtain estimates. The research shows that the bootstrap method produces reasonable estimators of standard errors in some sample survey problems. The bootstrap method overcomes some of the theoretical and practical difficulties of ordinary procedures in both the design based and prediction approach. Further study of the bootstrap in more complex designs and with other models may enhance the usefulness of the method for estimating standard errors.