hdquantile {Hmisc} | R Documentation

## 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

`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.

### 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

    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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