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Robust diagnostics for the heteroscedastic regression model

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. Atkinson, Anthony C. & Riani, Marco & Torti, Francesca, 2016. "Robust methods for heteroskedastic regression," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 209-222.
    4. 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.
    5. 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.

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