In article <IGc%5.22384$[EMAIL PROTECTED]>,
Alan Miller <amiller @ vic.bigpond.net.au> wrote:
>Stefan Oberhoff wrote in message <91jat3$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.
There is an extensive OLD literature on errors in both
variables. AFAIK, no methods to handle even a portion
of what can be done has been programmed. The "errors-
in-variables" programs assume that too much is known.
The systematic part being non-normal is enough to make
it possible.
But this is NOT the stated problem. The key assumptions
in the above is independence between errors and the
systematic part. If rounding is the cause of the errors,
this is very definitely NOT the case; other than linear
programming, I do not know of any approach to even the
non-statistical version of the problem.
--
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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