weighted regression

[David L Lorenz <lorenz@usgs.gov>]

  We have a situation where we
know the variance of observations for a linear regression problem and need
confidence limits on the parameter estimates. The documentation in the
NOTES section for lm states "In addition,
S-PLUS does not currently support weighted regression when the absolute
precision of the observations is known. This situation arises often
in physics and engineering, when the uncertainty associated with a particular
measurement is known in advance due to properties of the measuring procedure
or device. If you know the absolute precision of your observations, it
is possible to supply them to the weights
argument. This computes the correct coefficients for your model, but the
standard errors and other inference tools will be incorrect."
  I have searched the web, done
bibliographic searches, and even searched the documentation for a competing
product and I found nothing regarding the solution of this problem. I would
be surprised if this problem has not been solved because it should be a
high priority in physics. At least I remember it being an issue in physics
classes, if not in the engineering classes I took.
  Is anyone aware of an approach
to estimating the confidence limits of parameter estimates when the variance
of the observations is known? I think I can see a solution for the case
of equal known variance, but I don't know that I have the ability to apply
that to unequal variances.Thanks.
Dave