Heteroscedastic symmetrical linear models

We discuss in this paper heteroscedastic linear models with symmetrical errors. The symmetrical class includes all symmetrical continuous distributions such as normal, Student-t, power exponential, logistics I and II, contaminated normal, so on. The variety of error distributions with different kurtosis coefficients than the normal one may give more flexibility in the choice of an appropriate error distribution, particularly to accommodate outlying and influential observations. We derive a joint iterative process for estimating the location and dispersion coefficients and we discuss some robustness aspects of the maximum likelihood estimates against outlying and large variance observations. The score test proposed by Cook and Weisberg [1983. Diagnostics for heteroscedasticity in regression. Biometrika 70, 1–10] is generalized and some diagnostic procedures such as leverage, local influence and residual analysis are derived. Finally, a data set is analyzed under heteroscedastic linear models with normal and heavy-tailed error distributions.