Re: Basis for quadratic Taguchi Loss Function

[Myron Tribus <mtribus@earthlink.net>]

Carl, I once discussed loss functions a few times with Dr. Taguchi.  He
said hewas perplexed over what function to use for the "general" case.
He settled on the quadratic loss function as the simplest and most
likely to be useful.  It postulates that the loss is "zero" when you are
on target.  The loss then increases as you depart from the target in
either direction.
I discuss loss functions in my book, "Rational Descriptions, Decisions
and Designs" (Pergamon 1969).  
A loss function could be very one sided. Consider the "William Tell"
loss function.  If he shoots the apple off his son's head, the loss is
"zero".  If he shoots too high, the loss is the cost of an arrow.  If he
shoots too low, well, the cost might be incalculable.
Pessimists work with loss functions.  Optimists work with value
functions.

Loss functions  are not "scientific".  Loss functions are highly
personal.  To ascribe a loss function to society requires plenty of
hutzpah! 

Myron Tribus