Robust diagnostics for the heteroscedastic regression model
The assumption of equal variance in the normal regression model is not always appropriate.Â Cook and Weisberg (1983) provide a score test to detect heteroscedasticity, whileÂ 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 ofÂ Atkinson (1994) and the fast algorithm of Neykov etÂ al. (2007) are employed to find the resulting estimator. Simulation and real data examples are used to illustrate the performance of the proposed approach.
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- 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.
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- Zaman, Asad & Rousseeuw, Peter J. & Orhan, Mehmet, 2000. "Econometric applications of high-breakdown robust regression techniques," MPRA Paper 41529, University Library of Munich, Germany.
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- 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.
- 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.
- 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.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- 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.
- Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-65, May.
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