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