----- Forwarded message from Daniela Ichim -----
In a nonlinear (univariate) regression problem, specifically
a calibration problem in thermometrics, I have the problem of
testing whether a curve expressing a relationship between
Electrical Resistance and Temperature is monotone
versus the possibility of it having bumps inverting the monotonicity.
The problem of checking the existance of bumps becomes difficult
especially in the regions of sparse data.
I would like directions to the existing related statistical literature.
----- End of forwarded message from Daniela Ichim -----
I used to make such measurements for a living. We did NOT use
statistics!-) I think the errors in temperature measurements swamped
any errors in electrical measurements. We usually treated the
resistances as correct. If it had a bump, it had a bump! Generally
these correlated with known phase changes within the substance. For
certain kinds of changes, we could check by redoing the measurements,
but often there was hysteresis. For example, we may have annealed the
sample once we reached a certain temperature, and now its resistance
was lower than it had been before at cooler temperatures. So even
with the same physical piece of material there may have been no such
thing as "THE resistance at 745 Celsius".
If you wanted to look at multiple specimens of the "same" material,
that was another ball game. Some alloys produced in large quantities
(Armco iron) might be predictable. "Pure" materials could be tricky
as resistance might be quite sensitive to very small impurities.
I think the general conclusion is one that always applies, but much
more so here: there is no substitue for knowing the material. A
metalurgist might be more help than a statistician!-)
PS
I believe there used to be a Thermophysical Properties Research Center
at Purdue that gathered data on such things from all over the world.
_
| | Robert W. Hayden
| | Work: Department of Mathematics
/ | Plymouth State College MSC#29
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