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Robust, Smoothly Heterogeneous Variance Regression

Michael Cohen, Siddhartha R. Dalal and John W. Tukey
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 42, No. 2 (1993), pp. 339-353
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2986237
Stable URL: http://www.jstor.org/stable/2986237
Page Count: 15
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Robust, Smoothly Heterogeneous Variance Regression
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Abstract

Under the simple linear regression model, we consider two violations of the standard assumptions, namely heterogeneous variances and long-tailed error distributions, in an integrated manner. A new method for estimation is proposed which assumes only that the heterogeneity is a locally smooth function of the regressor variable, except for outliers. The procedure is based on smoothing the non-outlying residuals from a robust regression to provide weights for a weighted regression. Monte Carlo results, some theory and a real data example are given. It is shown that the method is substantially more efficient than the usual robust regression methods in the presence of heterogeneity and only slightly worse when the variances are exactly equal.

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