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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