1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
|
\name{hdquantile}
\alias{hdquantile}
\title{Harrell-Davis Distribution-Free Quantile Estimator}
\description{
Computes the Harrell-Davis (1982) quantile estimator and jacknife
standard errors of quantiles. The quantile estimator is a weighted
linear combination or order statistics in which the order statistics
used in traditional nonparametric quantile estimators are given the
greatest weight. In small samples the H-D estimator is more efficient
than traditional ones, and the two methods are asymptotically
equivalent. The H-D estimator is the limit of a bootstrap average as
the number of bootstrap resamples becomes infinitely large.
}
\usage{
hdquantile(x, probs = seq(0, 1, 0.25),
se = FALSE, na.rm = FALSE, names = TRUE, weights=FALSE)
}
\arguments{
\item{x}{a numeric vector}
\item{probs}{vector of quantiles to compute}
\item{se}{set to \code{TRUE} to also compute standard errors}
\item{na.rm}{set to \code{TRUE} to remove \code{NA}s from \code{x}
before computing quantiles}
\item{names}{set to \code{FALSE} to prevent names attributions from
being added to quantiles and standard errors}
\item{weights}{set to \code{TRUE} to return a \code{"weights"}
attribution with the matrix of weights used in the H-D estimator
corresponding to order statistics, with columns corresponding to
quantiles.}
}
\details{
A Fortran routine is used to compute the jackknife leave-out-one
quantile estimates. Standard errors are not computed for quantiles 0 or
1 (\code{NA}s are returned).
}
\value{
A vector of quantiles. If \code{se=TRUE} this vector will have an
attribute \code{se} added to it, containing the standard errors. If
\code{weights=TRUE}, also has a \code{"weights"} attribute which is a matrix.
}
\references{
Harrell FE, Davis CE (1982): A new distribution-free quantile
estimator. Biometrika 69:635-640.
Hutson AD, Ernst MD (2000): The exact bootstrap mean and variance of
an L-estimator. J Roy Statist Soc B 62:89-94.
}
\author{Frank Harrell}
\seealso{\code{\link{quantile}}}
\examples{
set.seed(1)
x <- runif(100)
hdquantile(x, (1:3)/4, se=TRUE)
\dontrun{
# Compare jackknife standard errors with those from the bootstrap
library(boot)
boot(x, function(x,i) hdquantile(x[i], probs=(1:3)/4), R=400)
}
}
\keyword{univar}
|
