R help - May 2003 - AW: approximation of CDF

> Almost any method of fitting a density estimate would work on 
> integrating (numerically) the result.
it is a nice idea concerning the monotony property, which 
will be obtained automatically, but I am going to use results 
of approximation analytically
> In particular, look at package polspline, where 
> p(old)logspline does the integration for you.
thank you, I am going to install it.
> >   is there any package in R capable of smooth approximation of CDF
> >   basing on given sample?  (Thus, I am not speaking about ecdf)
> 
> I think it _is_ an ECDF you want to approximate, since you mention
> `sample' below.
no, it is not. I do not need the closeness to a ECDF but to a CDF.
classic ECDF (like that implemented in stepfun) is yet another 
approximation of CDF. In particular, if I try to pursue the best 
approximation of any ECDF function in polynomial basis, it will 
boost order of my polynomial approximation up to infinity. Meanwhile 
the CDF might be linear in the corresponding range (we could take 
uniform data as an example)

thank you for your reply,
kind regards,
Valery A.Khamenya
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Bioinformatics Department
BioVisioN AG, Hannover

> 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
---------------------------------------------------------------------------
Bioinformatics Department
BioVisioN AG, Hannover