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Re: [Phys-l] Curve fitting versus averaging [was question on averaging]



On 02/19/2009 10:29 AM, Crawford MacCallum wrote:
I was taught one hundred years ago to average the
differences between position 0 and n/2, 1 and n/2 + 1, ...
thus using all the data.

Huh. That's ingenious. I've never heard of that before.

I compared the three methods
a) find the slope for adjacent pairs, then average
b) find the slope for pairs n/2 samples apart, then average
c) least-squares fit

I did a Monte Carlo with 100 samples of 100 data points each.

As for finding the slope, method (b) is of course worse than
method (c) ... but only very slightly so. I was surprised at
how slight the difference was. The noise on the estimated
slope was only about 20% more.

Meanwhile, method (a) was a disaster, as expected because of
the telescoping sum.

Similar words apply to estimating the y-intercept. Method (b)
was only about 20% worse than method (c).

thus using all the data.

That is of course not the criterion. In some sense method (a)
"uses" all the data; it's just not very smart about it.

==============

I can't really recommend method (b). It's not much worse than
a full-blown curve fit ... but on the other hand it's not
appreciably easier, either.