This dissertation is concerned with the evaluation of a robust modification of existing methodology
within the classical inference framework. This results in an F-test based on the robust
weights used in arriving at the M or Bounded-Influence estimates. These estimates are known to
be robust to outliers and highly influential points, respectively. The first part of this evaluation
involves a Monte Carlo power study, under violations of the classical assumptions, of this F-test
based on robust weights and several other proposed robust tests. It is shown in simulation studies
that, under certain conditions, the F-test based on robust weights is a much more powerful test than
the classical F -test, and compares favorably to all other proposals studied. The second part involves
the development of the influence curve (IC) for the F-test based on robust weights and one empirical
approximation to the IC, the Sample Influence Curve (SIC). It is shown for two sample
data sets that the SIC demonstrates the resistance to unusual points of the F-test based on robust
weights.
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