Michael Becher wrote:
Dear Professor Harrell,
please allow me a brief question about the wtd.quantile() function in
your marvelous R package Hmisc that I was not able to answer using the
documentation or the web. For type="quantile", what is the exact
statistic that is estimated? The documentation says that the same
interpolated order statistic as in the quantile() function is used. As
far as I can tell, the quantile() function has 5 different interpolated
order statistics (types 4-9). The default for quantile() is type 7 - is
the same used in wtd.quantile? Or is it tpye 8, which is recommended by
Hyndman and Fan (1996), since it is median unbiased and distribution
free? Or something else?
Thanks a lot for your attention.
Respectfully,
Michael
---
Michael Becher
Princeton University
Department of Politics
mbec...@princeton.edu
Here is an empirical way to answer the question, for the case where the
weights are all equal to 1. Methods could be said to be identical when
then maximum difference is < 1e-10. You can see that the default for
wtd.quantile equals the default for quantile. -Frank
require(Hmisc)
set.seed(1)
u <- eval(formals(wtd.quantile)$type)
v <- as.character(1:9)
r <- matrix(0, nrow=length(u), ncol=9, dimnames=list(u,v))
for(n in c(8, 13, 22, 29))
{
x <- rnorm(n)
for(i in 1:5) {
probs <- sort( runif(9))
for(wtype in u) {
wq <- wtd.quantile(x, type=wtype, weights=rep(1,length(x)),
probs=probs)
for(qtype in 1:9) {
rq <- quantile(x, type=qtype, probs=probs)
r[wtype, qtype] <- max(r[wtype,qtype], max(abs(wq-rq)))
}
}
}
}
r
1 2 3 4 5
6
quantile 0.5729927 0.5729927 0.7547948 5.022317e-01 0.3725233
6.416295e-01
(i-1)/(n-1) 0.5729927 0.5729927 0.7547948 5.022317e-01 0.3725233
6.416295e-01
i/(n+1) 0.7088892 0.7088892 0.8569561 7.195455e-01 0.3208148
4.440892e-16
i/n 0.7774653 0.7774653 0.4093181 4.440892e-16 0.4284780
7.195455e-01
7 8 9
quantile 0.000000e+00 0.4717554 0.4422707
(i-1)/(n-1) 8.881784e-16 0.4717554 0.4422707
i/(n+1) 6.416295e-01 0.2138765 0.2406111
i/n 5.022317e-01 0.5464169 0.5169322
--
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
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