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Robust diagnostics for the heteroscedastic regression model


  • Cheng, Tsung-Chi


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

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    References listed on IDEAS

    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.
    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. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1500-1529, December.
    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. 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.
    11. 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.
    12. 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.
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    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. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.


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