Bootstrap Confidence Interval for Model Based Sampling

Thomas Mageto; John Motubwa

doi:doi:10.11648/j.ajtas.20180704.13

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Bootstrap Confidence Interval for Model Based Sampling

Thomas Mageto, John Motubwa

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 4)

Received: 28 March 2018 Accepted: 15 April 2018 Published: 18 May 2018

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 4)
DOI	10.11648/j.ajtas.20180704.13
Page(s)	147-155
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Bootstrap, Model Based, Confidence Interval, Sample Surveys

References

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[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.
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[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.
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[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.
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Thomas Mageto, John Motubwa. (2018). Bootstrap Confidence Interval for Model Based Sampling. American Journal of Theoretical and Applied Statistics, 7(4), 147-155. https://doi.org/10.11648/j.ajtas.20180704.13

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ACS Style

Thomas Mageto; John Motubwa. Bootstrap Confidence Interval for Model Based Sampling. Am. J. Theor. Appl. Stat. 2018, 7(4), 147-155. doi: 10.11648/j.ajtas.20180704.13

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AMA Style

Thomas Mageto, John Motubwa. Bootstrap Confidence Interval for Model Based Sampling. Am J Theor Appl Stat. 2018;7(4):147-155. doi: 10.11648/j.ajtas.20180704.13

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@article{10.11648/j.ajtas.20180704.13,
  author = {Thomas Mageto and John Motubwa},
  title = {Bootstrap Confidence Interval for Model Based Sampling},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {4},
  pages = {147-155},
  doi = {10.11648/j.ajtas.20180704.13},
  url = {https://doi.org/10.11648/j.ajtas.20180704.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/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.},
 year = {2018}
}

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TY  - JOUR
T1  - Bootstrap Confidence Interval for Model Based Sampling
AU  - Thomas Mageto
AU  - John Motubwa
Y1  - 2018/05/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180704.13
DO  - 10.11648/j.ajtas.20180704.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 147
EP  - 155
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180704.13
AB  - 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.
VL  - 7
IS  - 4
ER  -

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Author Information

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

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Thomas Mageto, John Motubwa. (2018). Bootstrap Confidence Interval for Model Based Sampling. American Journal of Theoretical and Applied Statistics, 7(4), 147-155. https://doi.org/10.11648/j.ajtas.20180704.13

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ACS Style

Thomas Mageto; John Motubwa. Bootstrap Confidence Interval for Model Based Sampling. Am. J. Theor. Appl. Stat. 2018, 7(4), 147-155. doi: 10.11648/j.ajtas.20180704.13

Copy | Download

AMA Style

Thomas Mageto, John Motubwa. Bootstrap Confidence Interval for Model Based Sampling. Am J Theor Appl Stat. 2018;7(4):147-155. doi: 10.11648/j.ajtas.20180704.13

Copy | Download

@article{10.11648/j.ajtas.20180704.13,
  author = {Thomas Mageto and John Motubwa},
  title = {Bootstrap Confidence Interval for Model Based Sampling},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {4},
  pages = {147-155},
  doi = {10.11648/j.ajtas.20180704.13},
  url = {https://doi.org/10.11648/j.ajtas.20180704.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Bootstrap Confidence Interval for Model Based Sampling
AU  - Thomas Mageto
AU  - John Motubwa
Y1  - 2018/05/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180704.13
DO  - 10.11648/j.ajtas.20180704.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 147
EP  - 155
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180704.13
AB  - 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.
VL  - 7
IS  - 4
ER  -

Copy | Download