Archive
Special Issues

Volume 7, Issue 4, July 2018, Page: 147-155
Bootstrap Confidence Interval for Model Based Sampling
Thomas Mageto, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
John Motubwa, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Received: Mar. 28, 2018;       Accepted: Apr. 15, 2018;       Published: May 18, 2018
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.
Keywords
Bootstrap, Model Based, Confidence Interval, Sample Surveys
Thomas Mageto, John Motubwa, Bootstrap Confidence Interval for Model Based Sampling, American Journal of Theoretical and Applied Statistics. Vol. 7, No. 4, 2018, pp. 147-155. doi: 10.11648/j.ajtas.20180704.13
Reference
[1]
Chambers, R. L. (2011). Which Sample Strategy? A Review of Three Different Approaches, Centre for Statistical and Survey Methodology. University of Wollongong, Working Paper 09-11, 2011.
[2]
Chambers, R. L., and Dorfman, A. H. (2003). Robust Sample Survey Inference via Bootstrapping and Bias Correction: The Case of the Ratio Estimator. Southampton: Southampton Statistical Sciences Research Institute 21pp. (S3RI Methodology Working papers, M03/13).
[3]
Smith, T. M. (1976). The Foundations of Survey Sampling: A Review. Journal of the Royal Statistical Society, A 139, 183-204.
[4]
Smith, T. M. (1984). Sample Surveys: Present Position and Potential Development: Some Personal Views. Journal of the Royal Statistical Society, A 147, 208-221.
[5]
Nadaraya, E. (1964). On Estimating Regression. Theory Probability and Applications, 9 141-142.
[6]
Watson, G. S. (1964). Smooth Regression Analysis. Sankhya, A 359-372.
[7]
Cheng, P. E. (1994). Non-parametric Estimation of Mean Function with Data Missing at Random. Journal of the American Statistical Association, 89, 81-87.
[8]
Dorfman, A. H. (1992). Nonparametric Regression for Estimating Totals in Finite Populations. Proceedings of the Section on Survey Research Methods. American Statistical Association, 88, 622-625.
[9]
Opsomer, D. J., & Breidt, F. J. (2000). The Application of Local Polynomial Regression to Survey Sampling Estimation. Working Paper, Iowa State University, Department of Statistics.
[10]
Rao, J. N., & Wu, C. F. (1988). Resampling Inference with Complex Survey Data. Journal of American Statistical Association, 83, 231-241.
[11]
Do, K. A., & Kokie, P. (2001). Bootstrap Variance and Confidence Interval Estimation for Model-Based Surveys. Technical Report, ustralia National University.
[12]
Godambe, V. P. (1955). A Unified Theory of Sampling from Finite Populations. Journal of the Royal Statistical Society, Series B (Methodological), Vol. 17. No. 2 pp. 269-278.
[13]
Kim, T. H., & Christopher, M. (2003). Two Stage Quartile Regression when the First Stage is Based on Quartile Regression. Journal Statistical Association, 7, 218-231.
[14]
Mageto, T., & Zablon, A. (2018). Modeling Self Medication Risk Factors (A Case Study of Kiambu County, Kenya). American Journal of Theoretical and Applied Statistics, 7(2), 58-66.
[15]
Venables, W. N., & Ripley, B. D. (2002). Modern Applied Statistics with S. Springer.
[16]
Royall, M. R., & Cumberland, G. W. (2012). Variance Estimation in Finite Population Sampling. Journal of the American Statistical Association, 73:362, 351-358.
[17]
Royall, R. M., & Cumberland, W. G. (1981a). An Empirical Study of the Ratio Estimator and Estimators of its Variance. Journal of the American Statistical Association, 76, 66-77.
[18]
Helwig, E. N. (2017). Bootstrap Confidence Intervals. Minneapolis and Saint Paul: University of Minnesota (Twin Cities).
[19]
Puth, M.-T., Neuhauser, M., & Ruxton, D. G. (2015). On the Variety of Methods for Calculating Confidence Intervals by Bootstrapping. Journal of Animal Ecology, 84, 892-897.
[20]
Fox, J., & Sanford, W. (2017). Bootstrapping Regression Models in R. An Appendix to An R Companion to Applied Regression, pp. 1-20.
[21]
Cochran, G. W. (1992). Sampling Techniques. New Delhi: Wiley Eastern Limited.
[22]
Alexopoulos, C. E. (2010). Introduction to Multivariate Regression Analysis. Hippokratia, 14, 23-28.