Least squares is probably the best known method for fitting linear
models and by far the most widely used. Surprisingly, the discrete L 1
analogue, least absolute deviations (LAD) seems to have been considered
first. Possibly the LAD criterion was forced into the background because
of the com- putational difficulties associated with it. Recently there
has been a resurgence of interest in LAD. It was spurred on by work that
has resulted in efficient al- gorithms for obtaining LAD fits. Another
stimulus came from robust statistics. LAD estimates resist undue effects
from a feyv, large errors. Therefore. in addition to being robust, they
also make good starting points for other iterative, robust procedures.
The LAD criterion has great utility. LAD fits are optimal for linear
regressions where the errors are double exponential. However they also
have excellent properties well outside this narrow context. In addition
they are useful in other linear situations such as time series and
multivariate data analysis. Finally, LAD fitting embodies a set of ideas
that is important in linear optimization theory and numerical analysis.
viii PREFACE In this monograph we will present a unified treatment of
the role of LAD techniques in several domains. Some of the material has
appeared in recent journal papers and some of it is new. This
presentation is organized in the following way. There are three parts,
one for Theory, one for Applicatior.s and one for Algorithms.
