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Robust, Smoothly Heterogeneous Variance Regression
Author(s) -
Cohen Michael,
Dalal Siddhartha R.,
Tukey John W.
Publication year - 1993
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2986237
Subject(s) - statistics , regression , variance (accounting) , regression analysis , mathematics , econometrics , economics , accounting
SUMMARY 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.