Abstract
Abstract
New Thoughts on Using Elemental and Non-Elemental
Sets to Produce Robust Estimates of Regression
Coefficients
The idea of utilizing elemental sets in linear regression was
proposed in 1755, but
was not widely accepted due to computational burdens. Renewed
recent interest in this
topic was inspired by the appeal of robust regression, along with
the development of
modern computational environments. In this paper, different
weighting factors are
developed and applied for elemental regression. These weights
combine information
from influence statistics together with variance information
associated with elemental
sets, to down-weight subsets with outliers with a view toward
maintaining efficiency for
estimating regression coefficients. A new approach, called the
"Drop K" method, is
proposed and assessed in simulation studies. Instead of selecting
all unique elemental
subsets containing the minimal number of observations sufficient to
fit the desired model,
k observations are dropped from the original dataset to form each
subset, where k is the
number of suspected outliers. Estimators were again calculated
under different weights,
including those based on influential statistics and the variance of
estimators from each
set. The performance of this method is compared with that of
elemental regression, as
well as with a popular robust regression technique (the Huber
estimator) in simulation
studies. The Drop K approach performed better than the least square
estimators, and
appears to provide an appealing alternative to elemental regression
estimators.
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Table of Contents
Table of Contents
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