New Thoughts on Using Elemental and Non-Elemental Sets to Produce Robust Estimates of Regression Coefficients 公开

Jin, Chengyin (2012)

Permanent URL: https://etd.library.emory.edu/concern/etds/b8515p34c?locale=zh
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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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