RE: Basis for quadratic Taguchi Loss Function

[Jonathan Siegel <jmsiegel@yahoo.com>]

Bob,

I believe I'm going to need to give you two different
answers here.

If you want to know how the concepts of least squares
and loss functions historically developed, there's no
doubt that the technique of least squares existed long
before the theory of loss functions was developed.
Since the theory of loss functions was  developed in
part to help explain why least squares seems to work,
in this sense the Taguchi loss function is based on
the pre-existing least squares method.

But if you asked me how I should act as an applied
statistician, I would want to start by learning your
objectives, and then use techniques that are
appropriate for them. This means I would want to start
by assessing your loss function, and then use a
technique that works for that loss function. I don't
always do this, but I try to when I can. In this
sense, my choice of a particular technique is based on
the client's loss function.

Jonathan Siegel

> Can you explain how Least Squares estimation is
> "based on Taguchi's quadratic loss function".  I see
> corelation, but don't you think the idea of the loss
> function is somehow based on the thinking behind
> least squares estimation?
> Bob Wilson