Data Research, Vol. 2, Issue 2, Apr  2018, Pages 54-64; DOI: 10.31058/ 10.31058/

An Investigation of Bootstrap Methods in Parametric Estimations in Simple Linear Regression

, Vol. 2, Issue 2, Apr  2018, Pages 54-64.

DOI: 10.31058/

Acha, Chigozie K 1* , Nwabueze, Joy C. 1

1 Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

Received: 5 June 2018; Accepted: 25 June 2018; Published: 17 July 2018

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This study compares the bootstrap methods in parametric estimations in simple linear regression. To achieve this set objective theoretical datasets replicated from normal distribution with different ability levels were used. Simple linear regression (SLR) models were employed to fit the datasets and all the scores were considered.  Evidence showed that the original data set (O310Mt) without bootstrap resulted in a poor model with high bias. Results also showed that when the sample size was small ≤ 200, in almost all the different assessment conditions, the parametric bootstrap model (H311Mt) performed better than all of the parametric bootstrap models including (<em style=


Parametric Bootstrap, Linear Regression, Estimations, information Criteria, Models


© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


[1] Abney, S. Bootstrapping, ACL ’02 Proceedings of the 40th Annual Meeting of the Association for Computational Linguistics Philadelphia, Pennsylvania, USA, 2002, July 07-12.

[2] Alrasheedi, M. Parametric and Non-Parametric Bootstrap: A Simulation Study for a Linear Regression with Residuals from a Mixture of Laplace Distributions. European Scientific Journal, 2013, 9(12), 120-131.

[3] Acha, C.K. Impact of Housing and Age of Birds on Egg Production. International Journal of Numerical Mathematics, 2010, 5(2), 275-298.

[4] Acha, C.K. Regression and Principal Component Analyses: a Comparison Using Few Regressors. American Journal of Mathematics and Statistics, 2012a, 2(1), 1-5, DOI: 10.5923/j.ajms. 20120201.01.

[5] Acha, C.K. On two Methods of Analysis Balanced Incomplete Block Designs. Pakistan Journal of Statistics and Operation Research, 2012b, 8(4), 749-757.

[6] Acha, C.K. Parametric Bootstrap Methods for Parameter Estimation in SLR Models. International Journal of Econometrics and Financial Management, 2014a, 2(5), 175-179, DOI: 10.12691/ijefm-2-5-2. Available online at (accessed on 23 April 2017).

[7] Acha, C.K. Bootstrapping Normal and Binomial Distributions. International Journal of Econometrics and Financial Management, 2014b, 2(6), 253-256, Doi: 10.12691/ijefm-2-6-2.

[8] Cover, T.M.; Thomas, J.A. Elements of Information Theory. John Wiley and Sons. 2006, 254.

[9] Efron, B.; Tibshirani, R.J. An Introduction to the Bootstrap. Chapman and Hall, New York, 1993.

[10] Chernick, M.R. Bootstrap Methods: A Practitioners Guide. Wiley, New York, 1999.

[11] Acha, C.K.; Acha I. A Smooth Bootstrap Methods on External Sector Statistics. International Journal of Econometrics and Financial Management, 2015, 3(3), 115-120, DOI: 10.12691/ijefm-3-3-2.

[12] Chernick, M.R.; LaBudde, R. An Introduction to the Bootstrap with Applications in R Wiley, Hoboken, 2011.

[13] Acha, C.K.; Omekara, C.O. Towards Efficiency in the Residual and Parametric Bootstrap Techniques. American Journal of Theoretical and Applied Statistics, 2016, 5(5), 285-289, DOI: 10.11648/j.ajtas.20160505.16.

[14] Freedman, D.A. Bootstrapping regression models, Ann. Statist, 1981, 6, 1218-1228.

[15] Lehikoinen, A.; Saurola, P.; Byholm, P.; Linden, A.; Valkama, J. Life history event of euasian sparrow hawk in a changing climate. Journal of Avian Biology, 2010, 41, 627-636.

[16] Acha, I.A.; Acha, C.K. Interest Rates in Nigeria: An Analytical Perspective. Research Journal of Finance and Accounting, 2011, 2(3), 71-81.

[17] Chatfield, C. The Analysis of Time Series - An Introduction. 6th Edition; Chapman and Hall, London, UK, 2004. ISBN 9781584883173

[18] MacKay, D. Information Theory, Inference and Learning Algorithms. 1st Edition; Cambridge University Press; United Kingdom, 2003, 347-348. ISBN-10: 0521642981; ISBN-13: 978-0521642989.

[19] Wang, T.; Brennan, R.L. A modified frequency estimation equating method for the common-item nonequivalent groups design estimating random error in equipercentile equating. Applied Psychological Measurement, 2009, 33, 118-132.

[20] Davidson, R.; MacKinnon, J.G. ‘Bootstrap Methods in Econometrics’, in Patterson, K. and Mills, T.C. (eds), Palgrave Handbook of Econometrics: Volume 1 Theoretical Econometrics. Palgrave Macmillan, Basingstoke, 2006b, 812-38.

[21] Wang, T.; Lee, W.; Brennan, R.L.; Kolen, M.J. A comparison of frequency estimation and chained equipercentile methods under the common-item nonequivalent groups design. Applied Psychological Measurement, 2008, 32, 632-651.

[22] Akaike, H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1974, AC-19, 716-723.

[23] Schwarz G. Estimating the Dimension of a Model. The Annals of Statistics, 1978, 6(2), 461-464.

[24] Hannan, E.J.; B.G. Quinn. The Determination of the order of an Auto regression. Journal of the Royal Statistical Society, 1979, 41, 190-195.

[25] Acha C.K. Rescaling Residual Bootstrap and Wild Bootstrap. International Journal of Data Science and Analysis, 2016, 2(1), 7-14, DOI: 10.11648/j.ijdsa.20160201.12.

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