AW: [R] approximation of CDF
Khamenia, Valery
V.Khamenia at BioVisioN.de
Thu May 8 16:45:03 CEST 2003
> You may need to clarify your terminologies. My understanding is that
> function *approximation* is for the situation where you have
> x1,..., xn and f(x1), ..., f(xn), without any error (a numerical
> analysis problem). Function *estimation* is when f() is not known,
> but estimated from data (a statistical problem). Sounds like you
> need estimation, not approximation.
> (There's duality between the two, but they are different problems.)
more then clear, thank you. Indeed I have missed here that
f(x1), ..., f(xn) are usually *implied* to be without any error.
However except of this issue the difference is rather
symbolical. Indeed, for ordered data the only difference
between "estimation" and "approximation" is that the convergence
properties and the model adequacy are discussed in statistical
terms for "estimation", i.e. in terms of confidence intervals
and p-values. On the contrary, for "approximation" just the
metric (the functional being optimized) should be chosen
and not necessarily that this metric should be interpretable
in probabilistic terms. Indeed, we shouldn't
forget, that "degrees of freedom" (which really could make
a difference in this context) for ordered data have no sense,
therefore, the difference between those two terms is rather
symbolical and negligible.
Actually, I have really forgotten to say what are the
values which should be treated as "true values without
any error" Than we have just an approximation task. Or?..
thank you for a reasonable note,
kind regards,
Valery A.Khamenya
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Bioinformatics Department
BioVisioN AG, Hannover
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