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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- Cizek, P., 2004.
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2004-130, Tilburg University, Center for Economic Research.
- 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.
- Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
- 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.
- 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.
- Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-65, May.
- 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.
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