standard error for quantile

-----Original Message-----
From: Jim Lemon [mailto:jim at bitwrit.com.au]
Sent: Wednesday, October 31, 2012 9:56 AM
To: PIKAL Petr
Cc: r-help at r-project.org
Subject: Re: [R] standard error for quantile

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