Towards Efficiency in the Residual and Parametric Bootstrap Techniques

Acha Chigozie K.; Omekara Chukwuemeka O.

doi:doi:10.11648/j.ajtas.20160505.16

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Towards Efficiency in the Residual and Parametric Bootstrap Techniques

Acha Chigozie K., Omekara Chukwuemeka O.

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)

Received: 20 July 2016 Accepted: 30 July 2016 Published: 17 August 2016

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Abstract

There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI	10.11648/j.ajtas.20160505.16
Page(s)	285-289
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), 2016. Published by Science Publishing Group

Keywords

Residual Bootstrap, Efficiency, Sufficiency, Parametric Bootstrap, Technique

References

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[15]	Acha, C. K. (2014a) Parametric Bootstrap Methods for Parameter Estimation in SLR Models. International Journal of Econometrics and Financial Management, 2 (5), 175-179. Doi: 10.12691/ijefm-2-5-2.
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[19]	Wang, T. & Brennan, R. L. (2009). A modified frequency estimation equating method for the common-item nonequivalent groups design estimating random error in equipercentile equating. Applied Psychological Measurement, 33, 118-132.
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Acha Chigozie K., Omekara Chukwuemeka O. (2016). Towards Efficiency in the Residual and Parametric Bootstrap Techniques. American Journal of Theoretical and Applied Statistics, 5(5), 285-289. https://doi.org/10.11648/j.ajtas.20160505.16

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ACS Style

Acha Chigozie K.; Omekara Chukwuemeka O. Towards Efficiency in the Residual and Parametric Bootstrap Techniques. Am. J. Theor. Appl. Stat. 2016, 5(5), 285-289. doi: 10.11648/j.ajtas.20160505.16

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AMA Style

Acha Chigozie K., Omekara Chukwuemeka O. Towards Efficiency in the Residual and Parametric Bootstrap Techniques. Am J Theor Appl Stat. 2016;5(5):285-289. doi: 10.11648/j.ajtas.20160505.16

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@article{10.11648/j.ajtas.20160505.16,
  author = {Acha Chigozie K. and Omekara Chukwuemeka O.},
  title = {Towards Efficiency in the Residual and Parametric Bootstrap Techniques},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {285-289},
  doi = {10.11648/j.ajtas.20160505.16},
  url = {https://doi.org/10.11648/j.ajtas.20160505.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.16},
  abstract = {There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.},
 year = {2016}
}

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TY  - JOUR
T1  - Towards Efficiency in the Residual and Parametric Bootstrap Techniques
AU  - Acha Chigozie K.
AU  - Omekara Chukwuemeka O.
Y1  - 2016/08/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.16
DO  - 10.11648/j.ajtas.20160505.16
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  - 285
EP  - 289
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.16
AB  - There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.
VL  - 5
IS  - 5
ER  -

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Author Information

Acha Chigozie K.

Department of Statistics, Michael Okpara University of Agriculture Umudike, Umudike, Nigeria
Omekara Chukwuemeka O.

Department of Statistics, Michael Okpara University of Agriculture Umudike, Umudike, Nigeria

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Plain Text BibTeX RIS

APA Style

Acha Chigozie K., Omekara Chukwuemeka O. (2016). Towards Efficiency in the Residual and Parametric Bootstrap Techniques. American Journal of Theoretical and Applied Statistics, 5(5), 285-289. https://doi.org/10.11648/j.ajtas.20160505.16

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ACS Style

Acha Chigozie K.; Omekara Chukwuemeka O. Towards Efficiency in the Residual and Parametric Bootstrap Techniques. Am. J. Theor. Appl. Stat. 2016, 5(5), 285-289. doi: 10.11648/j.ajtas.20160505.16

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AMA Style

Acha Chigozie K., Omekara Chukwuemeka O. Towards Efficiency in the Residual and Parametric Bootstrap Techniques. Am J Theor Appl Stat. 2016;5(5):285-289. doi: 10.11648/j.ajtas.20160505.16

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@article{10.11648/j.ajtas.20160505.16,
  author = {Acha Chigozie K. and Omekara Chukwuemeka O.},
  title = {Towards Efficiency in the Residual and Parametric Bootstrap Techniques},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {285-289},
  doi = {10.11648/j.ajtas.20160505.16},
  url = {https://doi.org/10.11648/j.ajtas.20160505.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.16},
  abstract = {There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Towards Efficiency in the Residual and Parametric Bootstrap Techniques
AU  - Acha Chigozie K.
AU  - Omekara Chukwuemeka O.
Y1  - 2016/08/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.16
DO  - 10.11648/j.ajtas.20160505.16
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  - 285
EP  - 289
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.16
AB  - There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.
VL  - 5
IS  - 5
ER  -

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