>In mathematical terms the optimal bandwith for density estimation
>decreases at rate n^{-1/5}, while the one for distribution function
>decreases at rate n^{-1/3}, if n is the sample size. In practical terms,
>one must choose an appreciably smaller bandwidth in the second case
>than in the first one.Thanks a lot for your remark! I was not aware of the fact that the optimal bandwidths for density and distribution do not decrease at the same rate. >Besides the computational aspect, there is a statistical one: >the optimal choice of bandwidth for estimating the density function >is not optimal (and possibly not even jsut sensible) for estimating >the distribution function, and the stated problem is equivalent to >estimation of the distribution function. The given interval "0<x<3" was only an example, in fact I would like to estimate the probability for intervals such as "0<=x<1" , "1<=x<2" , "2<=x<3" , "3<=x<4" , .... and compare it with the estimates of a corresponding histogram. In this case the stated problem is not anymore equivalent to the estimation of the distribution function. What do you think, can I go a ahead in this case with the optimal bandwidth for the density? Thanks a lot for your help! Best wishes Pedro >best wishes, > >Adelchi > > >PR> >PR> > >PR> >-- >PR> >Gregory (Greg) L. Snow Ph.D. >PR> >Statistical Data Center >PR> >Intermountain Healthcare >PR> >[EMAIL PROTECTED] >PR> >(801) 408-8111 >PR> > >PR> > >PR> >-----Original Message----- >PR> >From: [EMAIL PROTECTED] >PR> >[mailto:[EMAIL PROTECTED] On Behalf Of Pedro >PR> >Ramirez Sent: Wednesday, June 07, 2006 11:00 AM >PR> >To: r-help@stat.math.ethz.ch >PR> >Subject: [R] Density Estimation >PR> > >PR> >Dear R-list, >PR> > >PR> >I have made a simple kernel density estimation by >PR> > >PR> >x <- c(2,1,3,2,3,0,4,5,10,11,12,11,10) >PR> >kde <- density(x,n=100) >PR> > >PR> >Now I would like to know the estimated probability that a new >PR> >observation falls into the interval 0<x<3. >PR> > >PR> >How can I integrate over the corresponding interval? >PR> >In several R-packages for kernel density estimation I did not >PR> >found a corresponding function. I could apply Simpson's Rule for >PR> >integrating, but perhaps somebody knows a better solution. >PR> > >PR> >Thanks a lot for help! >PR> > >PR> >Pedro >PR> > >PR> >_________ >PR> > >PR> >______________________________________________ >PR> >R-help@stat.math.ethz.ch mailing list >PR> >https://stat.ethz.ch/mailman/listinfo/r-help >PR> >PLEASE do read the posting guide! >PR> >http://www.R-project.org/posting-guide.html >PR> > >PR> >PR> ______________________________________________ >PR> R-help@stat.math.ethz.ch mailing list >PR> https://stat.ethz.ch/mailman/listinfo/r-help >PR> PLEASE do read the posting guide! >PR> http://www.R-project.org/posting-guide.html >PR> ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
