hdquantile: 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

 ```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 `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.

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.

`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) ```

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