Bootstrap Confidence Interval for Model Based Sampling

Thomas Mageto

doi:10.11648/j.ajtas.20180704.13

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.

Highlights

Sample survey theory is concerned with methods of sampling from finite population of N identifiable units and making inferences about finite population quantities on the basis of sample data
The procedures with less mean square error are considered better compared to the ones with higher mean square values in estimating finite population total
The study results provide great insight in constructing confidence interval for population total using family of nonparametric methods in which minimizing cross validation, unbiased cross validation and biased cross validation techniques interval methods as shown in Figure 2. perform better compared to rest of bootstrap confidence

Summary

Introduction

Sample survey theory is concerned with methods of sampling from finite population of N identifiable units and making inferences about finite population quantities on the basis of sample data. There are different approaches to specifying sampling strategy and these include, design based, model assisted and model based approaches In considering all these approaches [1] has suggested that the model-based approach performs better than the other two approaches no one single approach gives both efficiency and robustness. A more general super population model to construct bootstrap confidence interval for the population total under simple random sampling without replacement is considered. In evaluating bootstrap confidence intervals performance, the empirical work is based on data provided in [21]. It gives the number of inhabitants in 49 selected states in United States of America. The test statistic t =35.383 equivalent to p-value less than 0 is an indication of linear regression such that β1 ≠ 0 at α =0.05 level of significance.

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Conclusion