On 30-Oct-2012 13:46:17 PIKAL Petr wrote: > Dear all > > I have a question about quantiles standard error, partly practical > partly theoretical. I know that > > x<-rlnorm(100000, log(200), log(2)) > quantile(x, c(.10,.5,.99)) > > computes quantiles but I would like to know if there is any function to > find standard error (or any dispersion measure) of these estimated > values. > > And here is a theoretical one. I feel that when I compute median from > given set of values it will have lower standard error then 0.1 quantile > computed from the same set of values. > > Is it true? If yes can you point me to some reasoning? > > Thanks for all answers. > Regards > Petr > ["PS" deleted]
The general asymptotic result for the pth quantile (0<p<1) X.p of a sample of size n is that it is asymptotically Normally distributed with mean the pth quantile Q.p of the parent distribution and var(X.p) = p*(1-p)/(n*f(Q.p)^2) where f(x) is the probability density function of the parent distribution. This is not necessarily very helpful for small sample sizes (depending on the parent distribution). However, it is possible to obtain a general result giving an exact confidence interval for Q.p given the entire ordered sample, though there is only a restricted set of confidence levels to which it applies. If you'd like more detail about the above, I could write up derivations and make the write-up available. Hoping this helps, Ted. ------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@wlandres.net> Date: 30-Oct-2012 Time: 17:40:55 This message was sent by XFMail ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
