Bootstrap Confidence Interval for Model Based Sampling

Abstract

The bootstrap approach to statistical inference in sample surveys is an area which has seen considerable development in the recent past. In model based approach to sample survey theory the main interest has been to overcome the problem of robustness under misspecifications. The bootstrap method under restrictive model specifications has been suggested by some authors as a way of achieving this. In this study, bootstrap and conventional confidence intervals for the population total in model based surveys using the simple random sampling without replacement are constructed. This is to provide a better measure of uncertainty associated with estimates of population total as compared to the corresponding rival confidence intervals under restrictive model. In order to achieve this, generated bootstrap simulations for the population of interest in assumed general model are used. The bootstrap method is less cumbersome to apply and in terms of coverage performance in 95% confidence interval, the bootstrap method is better compared to corresponding one under conventional methods. In terms of length, the confidences generated by the bootstrap method are much smaller as compared to the conventional counterparts. It is noted that the best performing confidence interval is one whose coverage rate is close to the true population total and its length small. The study research results provides great insight in constructing better confidence interval for the finite population total estimators.