hdquantile: Harrell-Davis Distribution-Free Quantile Estimator

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/Misc.s

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

1
2
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 NAs 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 (NAs 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.

Author(s)

Frank Harrell

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

quantile

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
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)

## End(Not run)

Example output

Loading required package: lattice
Loading required package: survival
Loading required package: Formula
Loading required package: ggplot2

Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

    format.pval, round.POSIXt, trunc.POSIXt, units

     0.25      0.50      0.75 
0.3064350 0.5054821 0.7571213 
attr(,"se")
      0.25       0.50       0.75 
0.03931112 0.04878284 0.02997026 

Attaching package: 'boot'

The following object is masked from 'package:survival':

    aml

The following object is masked from 'package:lattice':

    melanoma


ORDINARY NONPARAMETRIC BOOTSTRAP


Call:
boot(data = x, statistic = function(x, i) hdquantile(x[i], probs = (1:3)/4), 
    R = 400)


Bootstrap Statistics :
     original        bias    std. error
t1* 0.3064350  0.0006562956  0.03920786
t2* 0.5054821  0.0058713474  0.04745287
t3* 0.7571213 -0.0024634346  0.02804352

Hmisc documentation built on Jan. 4, 2018, 3:22 a.m.