In article <91jat3$b51$04$[EMAIL PROTECTED]>,
Stefan Oberhoff <[EMAIL PROTECTED]> wrote:
>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.
This is a moderately complicated linear programming
problem. Methods using standard deviations or even sums
of absolute errors are not appropriate, and the errors of
observation are not independent of the actual values if
the procedure is of the rounding type when reading an
instrument.
The usual type of statistical procedure is not what should
be used for this type of problem. If the bounds on the
errors are known, one can get bounds for the regression, as
one can describe the set of all regressions which satisfy
the conditions, and has no basis for choosing between them
if the errors are uniform. If they are not known, the
problem is harder.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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