American Journal of Theoretical and Applied Statistics

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Towards Efficiency in the Residual and Parametric Bootstrap Techniques

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.

DOI 10.11648/j.ajtas.20160505.16
Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5, September 2016)
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), 2024. Published by Science Publishing Group

Keywords

Residual Bootstrap, Efficiency, Sufficiency, Parametric Bootstrap, Technique

References
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[3] Paparoditis, E., and Politis, D. N. (2001a). Tapered block bootstrap. Biometrika 88, 1105-1119.
[4] Lahiri, S. N. (2006). Bootstrap Methods: A Review. In Frontiers in Statistics (J. Fan and H. L. Koul, editors) 231-265, Imperial College Press, London.
[5] Paparoditis, E., and Politis, D. N. (2005). Bootstrapping unit root tests for autoregressive time series. J. Am. Statist. Assoc. 100, 545-553.
[6] Schimek, M. G. (2000) Smoothing and Regression. Wiley, Hoboken.
[7] Chernick, M. R. (1999). Bootstrap Methods: A Practitioners Guide. Wiley, New York.
[8] Chernick, M. R. and LaBudde, R. (2011). An Introduction to the Bootstrap with Applications in R Wiley, Hoboken.
[9] Paparoditis, E., and Politis, D. N. (2001b). A Markovian local resampling scheme for nonparametric estimators in time series analysis. Econ. Theory 1, 540-566.
[10] Paparoditis, E. (2005). Testing the fit of a vector autoregressive moving average model. J. Time Series Anal. 26, 543-568.
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[12] Politis, K. (2003). Semiparametric estimation for non-ruin probabilities. Scand. Act. J., 75-96.
[13] Wilcox, R., and Keselman, H. (2006). Detecting heteroscedasticity in a simple regression model via quantile regression slopes. J. Statist. Comput. Simul. 76, 705-712.
[14] William G. J. and David A. A. (2014), Bootstrap Confidence Regions for Multidimensional Scaling Solutions. American Journal of Political Science, 58 (1); 264-278.
[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.
[16] Acha, C. K. (2014b) Bootstrapping Normal and Binomial Distributions. International Journal of Econometrics and Financial Management, 2 (6), 253– 256. Doi: 10.12691/ijefm-2-6-2.
[17] Acha, C. K. and Acha I. A. (2015) Smooth Bootstrap Methods on External Sector Statistics. International Journal of Econometrics and Financial Management, 3 (3), 115–120. Doi: 10.12691/ijefm-3-3-2.
[18] Wang, T., Lee, W., Brennan, R. L. & Kolen, M. J. (2008). A comparison of frequency estimation and chained equipercentile methods under the common-item nonequivalent groups design. Applied Psychological Measurement, 32, 632-651.
[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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Author Information
  • Department of Statistics, Michael Okpara University of Agriculture Umudike, Umudike, Nigeria

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

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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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    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://download.sciencepg.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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