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Re: (zdog) Re: (4) Estimating continuous functions

by tilly (Archbishop)
on Mar 30, 2004 at 17:17 UTC ( #341027=note: print w/ replies, xml ) Need Help??

in reply to (zdog) Re: (4) Estimating continuous functions
in thread Estimating continuous functions

First of all for the general case, some back of the envelope estimates suggest to me that 1/distance is a better weighting than my original 1/distance**2.

As for your specific function, you may find it worthwhile to do some transformations first. For instance if I understand your description, then log(F(x,y,z)) is roughly of the form K*log(log(x))/(y*z). So log(F(x,y,z))*y*z/log(log(x)) is roughly a constant.

This is good because the estimator that I provided is going to give the best results when approximating functions that are roughly constant. (Cubic splines, etc, give very good results at approximating functions that locally look like low-degree polynomials.) And estimating this "rough constant" gives you (after reversing the above calculation) your original function F.

In general a judicious application of general theory and specific knowledge about your situation is more effective than abstract theory by itself...

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