[R] approximation of CDF

[Liaw, Andy]

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.)

As Prof. Ripley suggested, most density estimators give you proper
densities, so integrating those will give you a proper CDF, in addition to
the monotonicity property that you mentioned (e.g., f(-Inf)=0, f(Inf)=1).

Andy 

> From: Khamenia, Valery [mailto:V.Khamenia at BioVisioN.de]
> 
> > 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
> --------------------------------------------------------------
> -------------
> Bioinformatics Department
> BioVisioN AG, Hannover
> 
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