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Heteroscedastic symmetrical linear models. (English) Zbl 1378.62021

Summary: 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 R. D. Cook and S. Weisberg [Biometrika 70, 1–10 (1983; Zbl 0502.62063)] 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.

MSC:

62J05 Linear regression; mixed models
62F10 Point estimation

Citations:

Zbl 0502.62063

Software:

GLIM
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Full Text: DOI

References:

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