Outlier Resistant Model Robust Regression

Abstract

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.