Karen George, M. R. Osborne, G. A. Watson, and R. S. Womersley
Abstract:
A simplicial algorithm for the rank regression estimation problem
is described. An implementation incorporating a secant method
based line search has been made in Microsoft Visual Basic 4.0, and
it is suggested that object oriented programming techniques are
very suitable for this application. Experiments with redescending
scores (nonconvex objective functions) are reported. Contour and
surface plots of 2-D problems suggest that the objective function
rapidly becomes uni-modal as the number of data points increases. A
similar observation has been made by Womersley in the case of
censored 11 estimation. The simplicial algorithm has been used
to gather supporting data. It has proved remarkably robust in the
sense that very few failures have been recorded from the non-convex
cases it is not really designed to handle. Also, for some standard
data sets, it provides a single (and acceptable) answer from a
range of starting points. Results are presented which offer a
possible explanation of the observed robustness. This is supported
by a summary of the computational experience.
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