Stefan Oberhoff wrote in message <91jat3$b51$04$[EMAIL PROTECTED]>...
>Hello all!
>
>In natural sciences you often encounter absolute maximum errors resulting
>from inaccurate measuring instruments. Maximum errors also occur when you
>estimate how precicely you can read a scale of a measuring instrument. If
>you have a dataset with different absolute errors in the x-values and
>different absolute errors in the y-values, is it possible to fit a staight
>line to this dataset, taking into account these different errors? Can you
>estimate the (maximum) error of slope and constant term of the regression
>line? I know there's an iterative method [D. York, Can. J. Phys. 44,
>pp.1079, 1966 or http://www.uio.no/~olews/stat/lsq.html] concerning a
>similar problem, but this method refers to different standard deviations of
>x and y and thus supplies standard deviations of slope and constant term. I
>don't see any opportunity of using this method as, in this case, I have to
>consider absolute maximum errors. Does anybody know a method to handle this
>problem? Any comments, references etc. are welcome.
>
>Many thanks in advance!
>Stefan
>
There are two departures here from the standard linear
model assumptions:
1. There are errors in both the X and the Y measurements.
2. The errors have a non-normal distribution (sounds like
a uniform distribution).
It would be a major exercise to produce code to accommodate
both of these, but I suspect that the second is relatively
unimportant. Least squares is pretty robust against this
kind of departure from normality.
Have a look at Applied Statistics algorithm AS 286 for the
`errors-in-variables' problem. It can also handle non-linear
models.
The original can be downloaded from statlib:
http://lib.stat.cmu.edu
while a Fortran 90 version is available from one of my web
sites.
--
Alan Miller, Retired Scientist (Statistician)
CSIRO Mathematical & Information Sciences
Alan.Miller -at- vic.cmis.csiro.au
http://www.ozemail.com.au/~milleraj
http://users.bigpond.net.au/amiller/
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