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