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. I found mcmcse package which shall compute the standard error but which I could not make to work probably because I do not have recent R-devel version installed Error in eval(expr, envir, enclos) : could not find function ".getNamespace" Error : unable to load R code in package 'mcmcse' Error: package/namespace load failed for 'mcmcse' Maybe I will also something find in quantreg package, but I did not went through it yet.
Petr: 1. Not an R question. 2. You want the distribution of order statistics. Search on that. It's basically binomial/beta. -- Bert On Tue, Oct 30, 2012 at 6:46 AM, PIKAL Petr <petr.pikal at precheza.cz> 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. > I found mcmcse package which shall compute the standard error but which > I could not make to work probably because I do not have recent R-devel > version installed > > Error in eval(expr, envir, enclos) : > could not find function ".getNamespace" > Error : unable to load R code in package 'mcmcse' > Error: package/namespace load failed for 'mcmcse' > > Maybe I will also something find in quantreg package, but I did not > went through it yet. > > ______________________________________________ > R-help at 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.-- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
Petr, You can do: require(quantreg) summary(rq(x ~ 1, tau = c(.10,.50,.99)) url: www.econ.uiuc.edu/~roger Roger Koenker email rkoenker at uiuc.edu Department of Economics vox: 217-333-4558 University of Illinois fax: 217-244-6678 Urbana, IL 61801 On Oct 30, 2012, at 9:37 AM, Bert Gunter wrote:> Petr: > > 1. Not an R question. > > 2. You want the distribution of order statistics. Search on that. It's > basically binomial/beta. > > -- Bert > > On Tue, Oct 30, 2012 at 6:46 AM, PIKAL Petr <petr.pikal at precheza.cz> 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. >> I found mcmcse package which shall compute the standard error but which >> I could not make to work probably because I do not have recent R-devel >> version installed >> >> Error in eval(expr, envir, enclos) : >> could not find function ".getNamespace" >> Error : unable to load R code in package 'mcmcse' >> Error: package/namespace load failed for 'mcmcse' >> >> Maybe I will also something find in quantreg package, but I did not >> went through it yet. >> >> ______________________________________________ >> R-help at 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. > > > > -- > > Bert Gunter > Genentech Nonclinical Biostatistics > > Internal Contact Info: > Phone: 467-7374 > Website: > http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm > > ______________________________________________ > R-help at 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.
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.Harding at wlandres.net> Date: 30-Oct-2012 Time: 17:40:55 This message was sent by XFMail
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
Thanks Jim. After reinstall of new R version all mentioned packages work. I tested various functions which revealed that on my lognorm data there is no big difference in error of median or 10% quantile. I also found some function for quantile se computing in Hmisc package. Petr> -----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
The rank test inversion option that you are trying to use won't work with only one coefficient, and therefore with univariate quantiles, if you use summary(rq(rnorm(50) ~ 1, tau = .9), cov = TRUE) you will have better luck. url: www.econ.uiuc.edu/~roger Roger Koenker email rkoenker at uiuc.edu Department of Economics vox: 217-333-4558 University of Illinois fax: 217-244-6678 Urbana, IL 61801 On Oct 30, 2012, at 9:42 AM, Koenker, Roger W wrote:> Petr, > > You can do: > > require(quantreg) > summary(rq(x ~ 1, tau = c(.10,.50,.99)) > > > url: www.econ.uiuc.edu/~roger Roger Koenker > email rkoenker at uiuc.edu Department of Economics > vox: 217-333-4558 University of Illinois > fax: 217-244-6678 Urbana, IL 61801 > > On Oct 30, 2012, at 9:37 AM, Bert Gunter wrote: > >> Petr: >> >> 1. Not an R question. >> >> 2. You want the distribution of order statistics. Search on that. It's >> basically binomial/beta. >> >> -- Bert >> >> On Tue, Oct 30, 2012 at 6:46 AM, PIKAL Petr <petr.pikal at precheza.cz> 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. >>> I found mcmcse package which shall compute the standard error but which >>> I could not make to work probably because I do not have recent R-devel >>> version installed >>> >>> Error in eval(expr, envir, enclos) : >>> could not find function ".getNamespace" >>> Error : unable to load R code in package 'mcmcse' >>> Error: package/namespace load failed for 'mcmcse' >>> >>> Maybe I will also something find in quantreg package, but I did not >>> went through it yet. >>> >>> ______________________________________________ >>> R-help at 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. >> >> >> >> -- >> >> Bert Gunter >> Genentech Nonclinical Biostatistics >> >> Internal Contact Info: >> Phone: 467-7374 >> Website: >> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm >> >> ______________________________________________ >> R-help at 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. > > ______________________________________________ > R-help at 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.