Rescaling Residual Bootstrap and Wild Bootstrap

Acha Chigozie Kelechi

doi:doi:10.11648/j.ijdsa.20160201.12

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Rescaling Residual Bootstrap and Wild Bootstrap

Acha Chigozie Kelechi

Published in International Journal of Data Science and Analysis (Volume 2, Issue 1)

Received: 20 July 2016 Accepted: 14 October 2016 Published: 28 October 2016

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Abstract

This paper examines and discusses a comparative analysis of hypothetical data by using bootstrap methods. The residual and wild bootstrap methods, including their rescaled versions were applied on the data collected from a normal distribution with different ability levels to check whether they are significant at various assessment conditions. The wild bootstrap compared in this paper are from Mammen and Redamarche distributions. In addition their kernel density plot is used to ascertain the trends and the performance at the lower ends of the distributions for each bootstrap model and also the trend as sample size tends to infinity. To achieve this, each of the forms were represented by using at least one functional model each from hypothetical data sets of a particular bootstrap data generating process (DGP) method to illustrate how 8640 scenerios were estimated. The result shows that the Hypothetical Rescaled Residual (HRR) is found to be preferable to the Hypothetical Unrescaled Residual (HR) while Hypothetical Wild Redamarche Model (HRWR) is found to be preferable to the Hypothetical Wild Mammen model (HRWM) with reference to their bias, standard error and root mean square error (RMSE) at different levels of significance, that is, B=99, N(0,1), n1 & n3 = 10000, RMSE = -0.0004 &-0.0025 respectively. Aslo, B=99, N(0,1), n3 = 10000, RMSE = -0.0004. Even though at B=99, N(0,1), n2 = 10000, RMSE for HRWM (0.0601) is higher than HRWR (0.0595). In fact, across all the models, rescaled residual functional model out performed all other functional models considered in this paper. Also, the trends at the lower ends of the distributions for each bootstrap model shows that the empirical distributions of true distributions follow the chi-square distribution and also tends to normal distribution as sample size tends to inifinity.

Published in	International Journal of Data Science and Analysis (Volume 2, Issue 1)
DOI	10.11648/j.ijdsa.20160201.12
Page(s)	7-14
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

Rescaled, Bootstrap, Hypothetical Models, Mammen Distributions, Redamarche Distributions

References

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Acha Chigozie Kelechi. (2016). Rescaling Residual Bootstrap and Wild Bootstrap. International Journal of Data Science and Analysis, 2(1), 7-14. https://doi.org/10.11648/j.ijdsa.20160201.12

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Acha Chigozie Kelechi. Rescaling Residual Bootstrap and Wild Bootstrap. Int. J. Data Sci. Anal. 2016, 2(1), 7-14. doi: 10.11648/j.ijdsa.20160201.12

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Acha Chigozie Kelechi. Rescaling Residual Bootstrap and Wild Bootstrap. Int J Data Sci Anal. 2016;2(1):7-14. doi: 10.11648/j.ijdsa.20160201.12

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@article{10.11648/j.ijdsa.20160201.12,
  author = {Acha Chigozie Kelechi},
  title = {Rescaling Residual Bootstrap and Wild Bootstrap},
  journal = {International Journal of Data Science and Analysis},
  volume = {2},
  number = {1},
  pages = {7-14},
  doi = {10.11648/j.ijdsa.20160201.12},
  url = {https://doi.org/10.11648/j.ijdsa.20160201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20160201.12},
  abstract = {This paper examines and discusses a comparative analysis of hypothetical data by using bootstrap methods. The residual and wild bootstrap methods, including their rescaled versions were applied on the data collected from a normal distribution with different ability levels to check whether they are significant at various assessment conditions. The wild bootstrap compared in this paper are from Mammen and Redamarche distributions. In addition their kernel density plot is used to ascertain the trends and the performance at the lower ends of the distributions for each bootstrap model and also the trend as sample size tends to infinity. To achieve this, each of the forms were represented by using at least one functional model each from hypothetical data sets of a particular bootstrap data generating process (DGP) method to illustrate how 8640 scenerios were estimated. The result shows that the Hypothetical Rescaled Residual (HRR) is found to be preferable to the Hypothetical Unrescaled Residual (HR) while Hypothetical Wild Redamarche Model (HRWR) is found to be preferable to the Hypothetical Wild Mammen model (HRWM) with reference to their bias, standard error and root mean square error (RMSE) at different levels of significance, that is, B=99, N(0,1), n1 & n3 = 10000, RMSE = -0.0004 &-0.0025 respectively. Aslo, B=99, N(0,1), n3 = 10000, RMSE = -0.0004. Even though at B=99, N(0,1), n2 = 10000, RMSE for HRWM (0.0601) is higher than HRWR (0.0595). In fact, across all the models, rescaled residual functional model out performed all other functional models considered in this paper. Also, the trends at the lower ends of the distributions for each bootstrap model shows that the empirical distributions of true distributions follow the chi-square distribution and also tends to normal distribution as sample size tends to inifinity.},
 year = {2016}
}

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TY  - JOUR
T1  - Rescaling Residual Bootstrap and Wild Bootstrap
AU  - Acha Chigozie Kelechi
Y1  - 2016/10/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ijdsa.20160201.12
DO  - 10.11648/j.ijdsa.20160201.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 7
EP  - 14
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20160201.12
AB  - This paper examines and discusses a comparative analysis of hypothetical data by using bootstrap methods. The residual and wild bootstrap methods, including their rescaled versions were applied on the data collected from a normal distribution with different ability levels to check whether they are significant at various assessment conditions. The wild bootstrap compared in this paper are from Mammen and Redamarche distributions. In addition their kernel density plot is used to ascertain the trends and the performance at the lower ends of the distributions for each bootstrap model and also the trend as sample size tends to infinity. To achieve this, each of the forms were represented by using at least one functional model each from hypothetical data sets of a particular bootstrap data generating process (DGP) method to illustrate how 8640 scenerios were estimated. The result shows that the Hypothetical Rescaled Residual (HRR) is found to be preferable to the Hypothetical Unrescaled Residual (HR) while Hypothetical Wild Redamarche Model (HRWR) is found to be preferable to the Hypothetical Wild Mammen model (HRWM) with reference to their bias, standard error and root mean square error (RMSE) at different levels of significance, that is, B=99, N(0,1), n1 & n3 = 10000, RMSE = -0.0004 &-0.0025 respectively. Aslo, B=99, N(0,1), n3 = 10000, RMSE = -0.0004. Even though at B=99, N(0,1), n2 = 10000, RMSE for HRWM (0.0601) is higher than HRWR (0.0595). In fact, across all the models, rescaled residual functional model out performed all other functional models considered in this paper. Also, the trends at the lower ends of the distributions for each bootstrap model shows that the empirical distributions of true distributions follow the chi-square distribution and also tends to normal distribution as sample size tends to inifinity.
VL  - 2
IS  - 1
ER  -

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Author Information

Acha Chigozie Kelechi

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

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Acha Chigozie Kelechi. (2016). Rescaling Residual Bootstrap and Wild Bootstrap. International Journal of Data Science and Analysis, 2(1), 7-14. https://doi.org/10.11648/j.ijdsa.20160201.12

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ACS Style

Acha Chigozie Kelechi. Rescaling Residual Bootstrap and Wild Bootstrap. Int. J. Data Sci. Anal. 2016, 2(1), 7-14. doi: 10.11648/j.ijdsa.20160201.12

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Acha Chigozie Kelechi. Rescaling Residual Bootstrap and Wild Bootstrap. Int J Data Sci Anal. 2016;2(1):7-14. doi: 10.11648/j.ijdsa.20160201.12

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@article{10.11648/j.ijdsa.20160201.12,
  author = {Acha Chigozie Kelechi},
  title = {Rescaling Residual Bootstrap and Wild Bootstrap},
  journal = {International Journal of Data Science and Analysis},
  volume = {2},
  number = {1},
  pages = {7-14},
  doi = {10.11648/j.ijdsa.20160201.12},
  url = {https://doi.org/10.11648/j.ijdsa.20160201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20160201.12},
  abstract = {This paper examines and discusses a comparative analysis of hypothetical data by using bootstrap methods. The residual and wild bootstrap methods, including their rescaled versions were applied on the data collected from a normal distribution with different ability levels to check whether they are significant at various assessment conditions. The wild bootstrap compared in this paper are from Mammen and Redamarche distributions. In addition their kernel density plot is used to ascertain the trends and the performance at the lower ends of the distributions for each bootstrap model and also the trend as sample size tends to infinity. To achieve this, each of the forms were represented by using at least one functional model each from hypothetical data sets of a particular bootstrap data generating process (DGP) method to illustrate how 8640 scenerios were estimated. The result shows that the Hypothetical Rescaled Residual (HRR) is found to be preferable to the Hypothetical Unrescaled Residual (HR) while Hypothetical Wild Redamarche Model (HRWR) is found to be preferable to the Hypothetical Wild Mammen model (HRWM) with reference to their bias, standard error and root mean square error (RMSE) at different levels of significance, that is, B=99, N(0,1), n1 & n3 = 10000, RMSE = -0.0004 &-0.0025 respectively. Aslo, B=99, N(0,1), n3 = 10000, RMSE = -0.0004. Even though at B=99, N(0,1), n2 = 10000, RMSE for HRWM (0.0601) is higher than HRWR (0.0595). In fact, across all the models, rescaled residual functional model out performed all other functional models considered in this paper. Also, the trends at the lower ends of the distributions for each bootstrap model shows that the empirical distributions of true distributions follow the chi-square distribution and also tends to normal distribution as sample size tends to inifinity.},
 year = {2016}
}

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TY  - JOUR
T1  - Rescaling Residual Bootstrap and Wild Bootstrap
AU  - Acha Chigozie Kelechi
Y1  - 2016/10/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ijdsa.20160201.12
DO  - 10.11648/j.ijdsa.20160201.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 7
EP  - 14
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20160201.12
AB  - This paper examines and discusses a comparative analysis of hypothetical data by using bootstrap methods. The residual and wild bootstrap methods, including their rescaled versions were applied on the data collected from a normal distribution with different ability levels to check whether they are significant at various assessment conditions. The wild bootstrap compared in this paper are from Mammen and Redamarche distributions. In addition their kernel density plot is used to ascertain the trends and the performance at the lower ends of the distributions for each bootstrap model and also the trend as sample size tends to infinity. To achieve this, each of the forms were represented by using at least one functional model each from hypothetical data sets of a particular bootstrap data generating process (DGP) method to illustrate how 8640 scenerios were estimated. The result shows that the Hypothetical Rescaled Residual (HRR) is found to be preferable to the Hypothetical Unrescaled Residual (HR) while Hypothetical Wild Redamarche Model (HRWR) is found to be preferable to the Hypothetical Wild Mammen model (HRWM) with reference to their bias, standard error and root mean square error (RMSE) at different levels of significance, that is, B=99, N(0,1), n1 & n3 = 10000, RMSE = -0.0004 &-0.0025 respectively. Aslo, B=99, N(0,1), n3 = 10000, RMSE = -0.0004. Even though at B=99, N(0,1), n2 = 10000, RMSE for HRWM (0.0601) is higher than HRWR (0.0595). In fact, across all the models, rescaled residual functional model out performed all other functional models considered in this paper. Also, the trends at the lower ends of the distributions for each bootstrap model shows that the empirical distributions of true distributions follow the chi-square distribution and also tends to normal distribution as sample size tends to inifinity.
VL  - 2
IS  - 1
ER  -

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