[R] standard error for quantile

[Jim Lemon]

On 10/31/2012 12:46 AM, 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?
>
Hi Petr,
Using a resampling method, it depends upon the distribution of the 
values. If you have a "love-hate" distribution (bimodal and heavily 
weighted toward extreme values), the median standard error can be 
larger. Try this:

x<-sample(-5:5,1000,TRUE,
  prob=c(0.2,0.1,0.05,0.04,0.03,0.02,0.03,0.04,0.05,0.1,0.2))
x<-ifelse(x<0,x+runif(1000),x-runif(1000))
hist(x)
mcse.q(x, 0.1)
$est
[1] -3.481419

$se
[1] 0.06887319

mcse.q(x, 0.5)
$est
[1] 1.088475

$se
[1] 0.3440115

 > mcse.q(x, 0.1)
$est
[1] -3.481419

$se
[1] 0.06887319

Jim