A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers

Bolakale Abdul-Hameed; Oyeyemi Gafar Matanmi

doi:doi:10.11648/j.pamj.20211006.13

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A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers

Bolakale Abdul-Hameed, Oyeyemi Gafar Matanmi

Published in Pure and Applied Mathematics Journal (Volume 10, Issue 6)

Received: 1 November 2021 Accepted: 26 November 2021 Published: 29 December 2021

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Abstract

Heteroscedasticity is a problem that arises in regression analysis for a variety of causes. This problem impacts both the estimation and test procedures and it is therefore critical to be able to detect the problem and address it. The presence of outliers is a regular occurrence in data analysis and the detection of heteroscedasticity in the presence of outliers poses lots of difficulty for most of the existing methods. In this paper, a modified Breusch-Pagan test for heteroscedasticity in the presence of outliers was proposed. The modified test is obtained by substituting non-robust components in the Breusch-Pagan test with robust procedures which makes the modified Breusch-Pagan test to be unaffected by outliers. Monte Carlo simulations and real data sets were used to investigate the performance of the newly proposed test. The probability value (p–value) and power of all methods considered in this study were computed and the results indicate that the modified robust version of Breusch-Pagan test outperformed the previous tests significantly. The proposed modified Breusch-Pagan test is therefore recommended for testing for heteroscedasticity in linear regression diagnosis, especially when the data sets evidently contain outliers.

Published in	Pure and Applied Mathematics Journal (Volume 10, Issue 6)
DOI	10.11648/j.pamj.20211006.13
Page(s)	139-149
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

Heteroscedasticity, Outliers, Cook’s Distance, S-estimation, Modified Breusch-Pagan Test, Monte Carlo Simulations

References

[1]	Alih, E., & Ong, H. C. (2015): An outlier-resistant test for heteroscedasticity in linear models. Journal of Applied Statistics, 42 (8), 1617–1634.
[2]	Breusch, T. S. and Pagan A. R. (1979): A simple test for heteroscedasticity and random coefficient variation, Econometrica 47, 1287-1294.
[3]	Chatterjee, S. and Hadi A. S. (2006): Regression Analysis by Examples. 4th Edition, Wiley, New York.
[4]	Cook, R. D. (1977): Detection of Influential Observations in Linear Regression, Technometrics. American Statistical Association. 19 (1): 15–18. doi: 10.2307/1268249. JSTOR 1268249. MR 0436478.
[5]	Goldfeld, S. M. and Quandt R. E., (1965): Some tests for homoskedasticity. J. Am. Stat. Assoc., 60: 539-547. http://www.belkcollege.uncc.edu/cdepken/econ6090/readings/goldfeld-quandt-1965.pdf
[6]	Hampel, F. R., Ronchetti E. M., Rousseeuw P. J. and Stahel W. (1986): Robust Statistics: The Approach Based on Influence Function. 1st Edition, Wiley, New York, pp: 536. ISBN: 0471735779.
[7]	Kutner M. H., Nachtsheim C. J. and Neter J. (2004): Applied Linear Regression Models. 4th Edition, McGraw-Hill/Irwin, New York, pp: 701. ISBN: 0-07-301344-7.
[8]	Montgomery D., Peck E., and Vining G. (2001): Introduction to Linear Regression Analysis, Student Solutions Manual, Wiley Series in Probability and Statistics, Wiley, New York.
[9]	Pindyck R. and Rubinfeld D. (1998): Econometric Models and Economic Forecasts (Text Alone), Econometric Models and Economic Forecasts, McGraw-Hill Companies, New York.
[10]	Rana M. S., Midi H. and Imon A. H. M. R (2008): A Robust Modification of the Goldfeld-Quandt Test for the Detection of Heteroscedasticity in the Presence of Outliers, Journal of Mathematics and Statistics (4): 277-283, 2008.
[11]	Rousseeuw, P. J. and Leroy A. (1987): Robust Regression and Outlier Detection, 1st Edition, Wiley, New York, pp: 329. ISBN: 0471852333.
[12]	Spearman C. (1904): The proof and measurement of association between two things, American Journal of Psychology. 15 (1): 72–101. doi: 10.2307/1412159.
[13]	White H. (1980): A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econ.: J. Econ. Soc., pp. 817–838.

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Bolakale Abdul-Hameed, Oyeyemi Gafar Matanmi. (2021). A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers. Pure and Applied Mathematics Journal, 10(6), 139-149. https://doi.org/10.11648/j.pamj.20211006.13

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ACS Style

Bolakale Abdul-Hameed; Oyeyemi Gafar Matanmi. A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers. Pure Appl. Math. J. 2021, 10(6), 139-149. doi: 10.11648/j.pamj.20211006.13

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AMA Style

Bolakale Abdul-Hameed, Oyeyemi Gafar Matanmi. A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers. Pure Appl Math J. 2021;10(6):139-149. doi: 10.11648/j.pamj.20211006.13

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@article{10.11648/j.pamj.20211006.13,
  author = {Bolakale Abdul-Hameed and Oyeyemi Gafar Matanmi},
  title = {A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {6},
  pages = {139-149},
  doi = {10.11648/j.pamj.20211006.13},
  url = {https://doi.org/10.11648/j.pamj.20211006.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211006.13},
  abstract = {Heteroscedasticity is a problem that arises in regression analysis for a variety of causes. This problem impacts both the estimation and test procedures and it is therefore critical to be able to detect the problem and address it. The presence of outliers is a regular occurrence in data analysis and the detection of heteroscedasticity in the presence of outliers poses lots of difficulty for most of the existing methods. In this paper, a modified Breusch-Pagan test for heteroscedasticity in the presence of outliers was proposed. The modified test is obtained by substituting non-robust components in the Breusch-Pagan test with robust procedures which makes the modified Breusch-Pagan test to be unaffected by outliers. Monte Carlo simulations and real data sets were used to investigate the performance of the newly proposed test. The probability value (p–value) and power of all methods considered in this study were computed and the results indicate that the modified robust version of Breusch-Pagan test outperformed the previous tests significantly. The proposed modified Breusch-Pagan test is therefore recommended for testing for heteroscedasticity in linear regression diagnosis, especially when the data sets evidently contain outliers.},
 year = {2021}
}

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TY  - JOUR
T1  - A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers
AU  - Bolakale Abdul-Hameed
AU  - Oyeyemi Gafar Matanmi
Y1  - 2021/12/29
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211006.13
DO  - 10.11648/j.pamj.20211006.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 139
EP  - 149
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211006.13
AB  - Heteroscedasticity is a problem that arises in regression analysis for a variety of causes. This problem impacts both the estimation and test procedures and it is therefore critical to be able to detect the problem and address it. The presence of outliers is a regular occurrence in data analysis and the detection of heteroscedasticity in the presence of outliers poses lots of difficulty for most of the existing methods. In this paper, a modified Breusch-Pagan test for heteroscedasticity in the presence of outliers was proposed. The modified test is obtained by substituting non-robust components in the Breusch-Pagan test with robust procedures which makes the modified Breusch-Pagan test to be unaffected by outliers. Monte Carlo simulations and real data sets were used to investigate the performance of the newly proposed test. The probability value (p–value) and power of all methods considered in this study were computed and the results indicate that the modified robust version of Breusch-Pagan test outperformed the previous tests significantly. The proposed modified Breusch-Pagan test is therefore recommended for testing for heteroscedasticity in linear regression diagnosis, especially when the data sets evidently contain outliers.
VL  - 10
IS  - 6
ER  -

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Author Information

Bolakale Abdul-Hameed

Department of Statistics, University of Ilorin, Ilorin, Nigeria
Oyeyemi Gafar Matanmi

Department of Statistics, University of Ilorin, Ilorin, Nigeria

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APA Style

Bolakale Abdul-Hameed, Oyeyemi Gafar Matanmi. (2021). A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers. Pure and Applied Mathematics Journal, 10(6), 139-149. https://doi.org/10.11648/j.pamj.20211006.13

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ACS Style

Bolakale Abdul-Hameed; Oyeyemi Gafar Matanmi. A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers. Pure Appl. Math. J. 2021, 10(6), 139-149. doi: 10.11648/j.pamj.20211006.13

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AMA Style

Bolakale Abdul-Hameed, Oyeyemi Gafar Matanmi. A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers. Pure Appl Math J. 2021;10(6):139-149. doi: 10.11648/j.pamj.20211006.13

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@article{10.11648/j.pamj.20211006.13,
  author = {Bolakale Abdul-Hameed and Oyeyemi Gafar Matanmi},
  title = {A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {6},
  pages = {139-149},
  doi = {10.11648/j.pamj.20211006.13},
  url = {https://doi.org/10.11648/j.pamj.20211006.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211006.13},
  abstract = {Heteroscedasticity is a problem that arises in regression analysis for a variety of causes. This problem impacts both the estimation and test procedures and it is therefore critical to be able to detect the problem and address it. The presence of outliers is a regular occurrence in data analysis and the detection of heteroscedasticity in the presence of outliers poses lots of difficulty for most of the existing methods. In this paper, a modified Breusch-Pagan test for heteroscedasticity in the presence of outliers was proposed. The modified test is obtained by substituting non-robust components in the Breusch-Pagan test with robust procedures which makes the modified Breusch-Pagan test to be unaffected by outliers. Monte Carlo simulations and real data sets were used to investigate the performance of the newly proposed test. The probability value (p–value) and power of all methods considered in this study were computed and the results indicate that the modified robust version of Breusch-Pagan test outperformed the previous tests significantly. The proposed modified Breusch-Pagan test is therefore recommended for testing for heteroscedasticity in linear regression diagnosis, especially when the data sets evidently contain outliers.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - A Modified Breusch–Pagan Test for Detecting Heteroscedasticity in the Presence of Outliers
AU  - Bolakale Abdul-Hameed
AU  - Oyeyemi Gafar Matanmi
Y1  - 2021/12/29
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211006.13
DO  - 10.11648/j.pamj.20211006.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 139
EP  - 149
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211006.13
AB  - Heteroscedasticity is a problem that arises in regression analysis for a variety of causes. This problem impacts both the estimation and test procedures and it is therefore critical to be able to detect the problem and address it. The presence of outliers is a regular occurrence in data analysis and the detection of heteroscedasticity in the presence of outliers poses lots of difficulty for most of the existing methods. In this paper, a modified Breusch-Pagan test for heteroscedasticity in the presence of outliers was proposed. The modified test is obtained by substituting non-robust components in the Breusch-Pagan test with robust procedures which makes the modified Breusch-Pagan test to be unaffected by outliers. Monte Carlo simulations and real data sets were used to investigate the performance of the newly proposed test. The probability value (p–value) and power of all methods considered in this study were computed and the results indicate that the modified robust version of Breusch-Pagan test outperformed the previous tests significantly. The proposed modified Breusch-Pagan test is therefore recommended for testing for heteroscedasticity in linear regression diagnosis, especially when the data sets evidently contain outliers.
VL  - 10
IS  - 6
ER  -

Copy | Download