Restricted and Unrestricted Methods of Bootstrap Data Generating Processes

Acha Chigozie K.; Nwabueze Joy C.

doi:doi:10.11648/j.ijtam.20160202.24

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Restricted and Unrestricted Methods of Bootstrap Data Generating Processes

Acha Chigozie K., Nwabueze Joy C.

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)

Received: 30 October 2016 Accepted: 17 November 2016 Published: 21 December 2016

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Abstract

This study compares the restricted and unrestricted methods of bootstrap data generating processes (DGPs) on statistical inference. It used hypothetical datasets simulated from normal distribution with different ability levels. Data were analyzed using different bootstrap DGPs. In practice, it is advisable to use the restricted parametric bootstrap DGP models and thereafter, check the kernel density of the empirical distributions that are close to normal (at least not too skewed). In fact, 21600 scenarios were replicated 200 times using bootstrap DGPs and kernel density methods. This analysis was carried out using R-statistical package. The results show that in a situation where the distribution of a test is skewed, all the scores need to be taken into account, no matter how small the sample size and the bootstrap level are. Across all the conditions considered, models HR5UR and HPN5UR yielded much larger bias and standard error while the smallest bias values were associated with models HR5R (0.0619) and HPN5R (0.0624). The result confirms the fact that bootstrap DGPs are very vital in statistical inference.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.ijtam.20160202.24
Page(s)	121-126
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

Restricted, Bootstrap DGPs, Simulation, Unrestricted, Functional Model

References

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APA Style

Acha Chigozie K., Nwabueze Joy C. (2016). Restricted and Unrestricted Methods of Bootstrap Data Generating Processes. International Journal of Theoretical and Applied Mathematics, 2(2), 121-126. https://doi.org/10.11648/j.ijtam.20160202.24

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ACS Style

Acha Chigozie K.; Nwabueze Joy C. Restricted and Unrestricted Methods of Bootstrap Data Generating Processes. Int. J. Theor. Appl. Math. 2016, 2(2), 121-126. doi: 10.11648/j.ijtam.20160202.24

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AMA Style

Acha Chigozie K., Nwabueze Joy C. Restricted and Unrestricted Methods of Bootstrap Data Generating Processes. Int J Theor Appl Math. 2016;2(2):121-126. doi: 10.11648/j.ijtam.20160202.24

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@article{10.11648/j.ijtam.20160202.24,
  author = {Acha Chigozie K. and Nwabueze Joy C.},
  title = {Restricted and Unrestricted Methods of Bootstrap Data Generating Processes},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {121-126},
  doi = {10.11648/j.ijtam.20160202.24},
  url = {https://doi.org/10.11648/j.ijtam.20160202.24},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.24},
  abstract = {This study compares the restricted and unrestricted methods of bootstrap data generating processes (DGPs) on statistical inference. It used hypothetical datasets simulated from normal distribution with different ability levels. Data were analyzed using different bootstrap DGPs. In practice, it is advisable to use the restricted parametric bootstrap DGP models and thereafter, check the kernel density of the empirical distributions that are close to normal (at least not too skewed). In fact, 21600 scenarios were replicated 200 times using bootstrap DGPs and kernel density methods. This analysis was carried out using R-statistical package. The results show that in a situation where the distribution of a test is skewed, all the scores need to be taken into account, no matter how small the sample size and the bootstrap level are. Across all the conditions considered, models HR5UR and HPN5UR yielded much larger bias and standard error while the smallest bias values were associated with models HR5R (0.0619) and HPN5R (0.0624). The result confirms the fact that bootstrap DGPs are very vital in statistical inference.},
 year = {2016}
}

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TY - JOUR
T1 - Restricted and Unrestricted Methods of Bootstrap Data Generating Processes
AU - Acha Chigozie K.
AU - Nwabueze Joy C.
Y1 - 2016/12/21
PY - 2016
N1 - https://doi.org/10.11648/j.ijtam.20160202.24
DO - 10.11648/j.ijtam.20160202.24
T2 - International Journal of Theoretical and Applied Mathematics
JF - International Journal of Theoretical and Applied Mathematics
JO - International Journal of Theoretical and Applied Mathematics
SP - 121
EP - 126
PB - Science Publishing Group
SN - 2575-5080
UR - https://doi.org/10.11648/j.ijtam.20160202.24
AB - This study compares the restricted and unrestricted methods of bootstrap data generating processes (DGPs) on statistical inference. It used hypothetical datasets simulated from normal distribution with different ability levels. Data were analyzed using different bootstrap DGPs. In practice, it is advisable to use the restricted parametric bootstrap DGP models and thereafter, check the kernel density of the empirical distributions that are close to normal (at least not too skewed). In fact, 21600 scenarios were replicated 200 times using bootstrap DGPs and kernel density methods. This analysis was carried out using R-statistical package. The results show that in a situation where the distribution of a test is skewed, all the scores need to be taken into account, no matter how small the sample size and the bootstrap level are. Across all the conditions considered, models HR5UR and HPN5UR yielded much larger bias and standard error while the smallest bias values were associated with models HR5R (0.0619) and HPN5R (0.0624). The result confirms the fact that bootstrap DGPs are very vital in statistical inference.
VL - 2
IS - 2
ER -

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Author Information

Acha Chigozie K.

Department of Statistics, Michael Okpara University of Agriculture, Umudike, Nigeria
Nwabueze Joy C.

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

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APA Style

Acha Chigozie K., Nwabueze Joy C. (2016). Restricted and Unrestricted Methods of Bootstrap Data Generating Processes. International Journal of Theoretical and Applied Mathematics, 2(2), 121-126. https://doi.org/10.11648/j.ijtam.20160202.24

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ACS Style

Acha Chigozie K.; Nwabueze Joy C. Restricted and Unrestricted Methods of Bootstrap Data Generating Processes. Int. J. Theor. Appl. Math. 2016, 2(2), 121-126. doi: 10.11648/j.ijtam.20160202.24

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AMA Style

Acha Chigozie K., Nwabueze Joy C. Restricted and Unrestricted Methods of Bootstrap Data Generating Processes. Int J Theor Appl Math. 2016;2(2):121-126. doi: 10.11648/j.ijtam.20160202.24

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@article{10.11648/j.ijtam.20160202.24,
  author = {Acha Chigozie K. and Nwabueze Joy C.},
  title = {Restricted and Unrestricted Methods of Bootstrap Data Generating Processes},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {121-126},
  doi = {10.11648/j.ijtam.20160202.24},
  url = {https://doi.org/10.11648/j.ijtam.20160202.24},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.24},
  abstract = {This study compares the restricted and unrestricted methods of bootstrap data generating processes (DGPs) on statistical inference. It used hypothetical datasets simulated from normal distribution with different ability levels. Data were analyzed using different bootstrap DGPs. In practice, it is advisable to use the restricted parametric bootstrap DGP models and thereafter, check the kernel density of the empirical distributions that are close to normal (at least not too skewed). In fact, 21600 scenarios were replicated 200 times using bootstrap DGPs and kernel density methods. This analysis was carried out using R-statistical package. The results show that in a situation where the distribution of a test is skewed, all the scores need to be taken into account, no matter how small the sample size and the bootstrap level are. Across all the conditions considered, models HR5UR and HPN5UR yielded much larger bias and standard error while the smallest bias values were associated with models HR5R (0.0619) and HPN5R (0.0624). The result confirms the fact that bootstrap DGPs are very vital in statistical inference.},
 year = {2016}
}

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