Re: Comparing LS and TLS


In article <7a685344-40b6-46be-a3a2-68138380bbfe@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
spasmous <spasmous@xxxxxxxxx> writes:
On Mar 25, 12:58=A0pm, Gordon Sande <g.sa...@xxxxxxxxxxxxxxxx> wrote:
On 2008-03-25 16:38:27 -0300,spasmous<spasm...@xxxxxxxxx> said:

I wrote some code to test the total least squares method. Results were
disappointing: for 10000 trials with different added Gaussian noise
the least squares produces the smallest error. When there are multiple
right hand side vectors there is a specific algorithm for TLS, which I
also compared (Ref Golub & van Loan). Results of this were worse than
LS and randomly better or worse than single RHS TLS.

I'm curious why is the special purpose TLS for multiple RHS not the
best? And why LS is superior to either TLS approach?!?

Numerical analysis will tell you HOW to compute it.
Statistics will tell you WHY you might want to compute it.

Why would you ask a statistics question in a numerical analysis newsgroup?=

Try sci.stat.math for a meaningful response. Do not be surprised to find
that you have not asked the question in a sensible way. Operationally
that means that you may not have actually done the experiment you think
you did.

When do you think TLS is called for? Hint: What errors do you have in the
predictors?


You're master of the vaguely negative comment that implies the poster
is a fool, so point scored there. But seriously what is wrong with the
simulation I posted? I honestly didn't understand the remarks in your
earlier post, please can you point out something specific wrong :)

I think his remark stated that your question already was without sense
in the setting you gave us:
in LS, one assumes the matrix non stochastic and exact, and the right hand
side with errors normally and indipendently distributed with mean zero
and variance sigma say. then the least squares solution has as expectation
value the "true" x.
in TLS A and b have errors, again of the same structure as above,
the "true" system is compatible and then the expectation value of the
TLS residual is zero.
but you "complained" about the effect, that the _actual_ error of
the TLS (in your experiment) was worse than the _actual_ LS solution error.
this makes no sense: there is no statement about the quality of the
actual error in x with the exception of confidence intervals, given some
level of propability for a error level

hth
peter

.

Relevant Pages

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