The approach you seem to want to take was great up to about 1950, but is silly
now. BC (Before Computers), many made restrictive assumptions concerning the
error terms to develop an elegant set of mathematical approaches to dealing with
distributions on the estimates. These days, you can toss the assumptions, and
get far more insight, with less hassle, through resampling (bootstrapping, etc.)
Resampling is an idea that tosses aside distributional assumptions about the
"error" terms. It lets the data speak for itself. It uses Monte Carlo
simulation, with some adjustments, to fit the model and to gain insight into the
distribution of the estimators. It is easy to implement, fast to run, and a
hell of a lot better than pre-supposing distributions of error terms for
mathematical convenience. It has shown itself to be far superior to "classical"
techniques in many important cases, and never worse, and has led people to make
decisions they would not have made otherwise (all of which turned out good, by
the way).
Minimizing least squares is a holdover from the days when it was far easier to
use than the abs deviation, which is more robust. KS is Kolmogorov-Smirnov.
R2 (hopefully adjusted) is related to techniques that, IMHO, should have been
road-kill by now, but there are a lot of semi-trained statisticians who
promulgate old ideas, and seem unwilling to keep up with the remarkable
developments in the last 20 years.
