# hdquantile

##### Harrell-Davis Distribution-Free Quantile Estimator

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.

- Keywords
- univar

##### Usage

```
hdquantile(x, probs = seq(0, 1, 0.25),
se = FALSE, na.rm = FALSE, names = TRUE, weights=FALSE)
```

##### Arguments

- x
a numeric vector

- probs
vector of quantiles to compute

- se
set to

`TRUE`

to also compute standard errors- na.rm
set to

`TRUE`

to remove`NA`

s from`x`

before computing quantiles- names
set to

`FALSE`

to prevent names attributions from being added to quantiles and standard errors- weights
set to

`TRUE`

to return a`"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 (`NA`

s are returned).

##### Value

A vector of quantiles. If `se=TRUE`

this vector will have an
attribute `se`

added to it, containing the standard errors. If
`weights=TRUE`

, also has a `"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.

##### See Also

##### Examples

```
# NOT RUN {
set.seed(1)
x <- runif(100)
hdquantile(x, (1:3)/4, se=TRUE)
# }
# NOT RUN {
# 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)
# }
```

*Documentation reproduced from package Hmisc, version 4.0-3, License: GPL (>= 2)*