Outlier Resistant Model Robust Regression

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Date
1997-04-14Author
Assaid, Christopher Ashley
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Show full item recordAbstract
Parametric regression fitting (such as OLS) to a data set
requires specification of an underlying model. If the
specified model is different from the true model, then the
parametric fit suffers to a degree that varies with the extent
of model misspecification. Mays and Birch (1996)
addressed this problem in the one regressor variable case
with a method known as Model Robust Regression
(MRR), which is a weighted average of independent
parametric and nonparametric fits to the data. This paper
was based on the underlying assumption of "well-behaved"
(Normal) data. The method seeks to take advantage of the
beneficial aspects of the both techniques: the parametric,
which makes use of the prior knowledge of the researcher
via a specified model, and the nonparametric, which is not
restricted by a (possibly misspecified) underlying model.
The method introduced here (termed Outlier Resistant
Model Robust Regression (ORMRR)) addresses the
situation that arises when one cannot assume well-behaved
data that vary according to a Normal distribution.
ORMRR is a blend of a robust parametric fit, such as
M-estimation, with a robust nonparametric fit, such as
Loess. Some properties of the method will be discussed as
well as illustrated with several examples.
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