IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i4p1845-1866.html

Robust diagnostics for the heteroscedastic regression model

Author

Listed:
  • Cheng, Tsung-Chi

Abstract

The assumption of equal variance in the normal regression model is not always appropriate. Cook and Weisberg (1983) provide a score test to detect heteroscedasticity, while Patterson and Thompson (1971) propose the residual maximum likelihood (REML) estimation to estimate variance components in the context of an unbalanced incomplete-block design. REML is often preferred to the maximum likelihood estimation as a method of estimating covariance parameters in a linear model. However, outliers may have some effect on the estimate of the variance function. This paper incorporates the maximum trimming likelihood estimation ([Hadi and Luceño, 1997] and [Vandev and Neykov, 1998]) in REML to obtain a robust estimation of modelling variance heterogeneity. Both the forward search algorithm of Atkinson (1994) and the fast algorithm of Neykov et al. (2007) are employed to find the resulting estimator. Simulation and real data examples are used to illustrate the performance of the proposed approach.

Suggested Citation

  • Cheng, Tsung-Chi, 2011. "Robust diagnostics for the heteroscedastic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1845-1866, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1845-1866
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00452-4
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Peide Shi & Chih‐Ling Tsai, 2002. "Regression model selection—a residual likelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 237-252, May.
    2. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    3. Hadi, Ali S. & Luceno, Alberto, 1997. "Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 25(3), pages 251-272, August.
    4. Murray Aitkin, 1987. "Modelling Variance Heterogeneity in Normal Regression Using GLIM," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 332-339, November.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Vandev, D., 1993. "A note on the breakdown point of the least median of squares and least trimmed squares estimators," Statistics & Probability Letters, Elsevier, vol. 16(2), pages 117-119, January.
    7. Cheng, Tsung-Chi & Biswas, Atanu, 2008. "Maximum trimmed likelihood estimator for multivariate mixed continuous and categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2042-2065, January.
    8. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    9. Cheng, Tsung-Chi, 2005. "Robust regression diagnostics with data transformations," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 875-891, June.
    10. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    11. Wen, Miin-Jye & Chen, Shun-Yi & Chen, Hubert J., 2007. "On testing a subset of regression parameters under heteroskedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5958-5976, August.
    12. Zaman, Asad & Rousseeuw, Peter J. & Orhan, Mehmet, 2001. "Econometric applications of high-breakdown robust regression techniques," Economics Letters, Elsevier, vol. 71(1), pages 1-8, April.
    13. Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Neykov, N.M. & Filzmoser, P. & Neytchev, P.N., 2012. "Robust joint modeling of mean and dispersion through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 34-48, January.
    2. Atkinson, Anthony C. & Riani, Marco & Torti, Francesca, 2016. "Robust methods for heteroskedastic regression," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 209-222.
    3. Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Moreno-Rebollo, J.L. & Muñoz-Pichardo, J.M., 2012. "Case-deletion type diagnostics for calibration estimators in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2219-2236.
    4. Conceição Amado & Ana M. Bianco & Graciela Boente & Isabel M. Rodrigues, 2025. "Robust estimation of heteroscedastic regression models: a brief overview and new proposals," Statistical Papers, Springer, vol. 66(3), pages 1-30, April.
    5. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.
    2. Cheng, Tsung-Chi & Biswas, Atanu, 2008. "Maximum trimmed likelihood estimator for multivariate mixed continuous and categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2042-2065, January.
    3. Chalabi, Yohan / Y. & Wuertz, Diethelm, 2010. "Weighted trimmed likelihood estimator for GARCH models," MPRA Paper 26536, University Library of Munich, Germany.
    4. Neykov, N.M. & Čížek, P. & Filzmoser, P. & Neytchev, P.N., 2012. "The least trimmed quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1757-1770.
    5. Chen, Songnian & Khan, Shakeeb, 2000. "Estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, vol. 98(2), pages 283-316, October.
    6. Machado, José A.F. & Santos Silva, J.M.C., 2019. "Quantiles via moments," Journal of Econometrics, Elsevier, vol. 213(1), pages 145-173.
    7. Gaglianone, Wagner Piazza & Guillén, Osmani Teixeira de Carvalho & Figueiredo, Francisco Marcos Rodrigues, 2018. "Estimating inflation persistence by quantile autoregression with quantile-specific unit roots," Economic Modelling, Elsevier, vol. 73(C), pages 407-430.
    8. Variyam, Jayachandran N., 2001. "Wic Participation And The Nutrient Intake Of Preschoolers," 2001 Annual meeting, August 5-8, Chicago, IL 20623, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    9. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    10. Shahidur R. Khandker & Zaid Bakht & Gayatri B. Koolwal, 2009. "The Poverty Impact of Rural Roads: Evidence from Bangladesh," Economic Development and Cultural Change, University of Chicago Press, vol. 57(4), pages 685-722, July.
    11. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
    12. Zaheer Anwer & Ashraf Khan & Muhammad Abubakr Naeem & Aviral Kumar Tiwari, 2025. "Modelling systemic risk of energy and non-energy commodity markets during the COVID-19 pandemic," Annals of Operations Research, Springer, vol. 345(2), pages 1193-1227, February.
    13. Narula, Subhash C. & Wellington, John F. & Lewis, Stephen A., 2012. "Valuating residential real estate using parametric programming," European Journal of Operational Research, Elsevier, vol. 217(1), pages 120-128.
    14. RAMDANI, Dendi & VAN WITTELOOSTUIJN, Arjen, 2009. "Board independence, CEO duality and firm performance: A quantile regression analysis for Indonesia, Malaysia, South Korea and Thailand," Working Papers 2009004, University of Antwerp, Faculty of Business and Economics.
    15. Pedro Telhado Pereira & Pedro Silva Martins, 2000. "Does education reduce wage inequality? Quantile regressions evidence from fifteen European countries," Nova SBE Working Paper Series wp379, Universidade Nova de Lisboa, Nova School of Business and Economics.
    16. Arjun & Bibhuti Ranjan Mishra, 2025. "Asymmetric role of environmental policy stringency, fiscal, and monetary policy on environmental sustainability: Evidence from BRICS‐T countries," Natural Resources Forum, Blackwell Publishing, vol. 49(2), pages 1187-1218, May.
    17. Shaoyu Li & Yanqing Sun & Liyang Diao & Xue Wang, 2021. "Distance-Based Analysis with Quantile Regression Models," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 291-312, July.
    18. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    19. Hirvonen, Lalaina, 2006. "Intergenerational Earnings Mobility Among Daughters and Sons: Evidence from Sweden and a Comparison with the United States," Working Paper Series 5/2006, Stockholm University, Swedish Institute for Social Research.
    20. Baris Kocaarslan & Ugur Soytas, 2025. "How do the reserve currency and uncertainties in major markets affect the uncertainty of oil prices over time?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 30(2), pages 2016-2041, April.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1845-1866. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.