AW: [R] approximation of CDF

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