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Tukey's Biweight Mean

Source: R/tukeyBiweight.R
tukeyBiweight.Rd

Computes Tukey's biweight robust mean (also known as the bisquare mean) of a numeric vector, optionally with a bootstrap confidence interval.

Usage

tukeyBiweight(
  x,
  conf.level = NA,
  sides = c("two.sided", "left", "right"),
  const = 9,
  na.rm = FALSE,
  ...
)

Arguments

x

a non-empty numeric vector of data values

conf.level

confidence level of the interval. If set to NA (the default), only the point estimate is returned.

sides

character string specifying the sidedness of the confidence interval (one of "two.sided" (default), "left" or "right"). See ConfidenceIntervals().

const

tuning constant passed to tbrm_cpp(). Defaults to 9.

na.rm

logical. Should missing values be removed before computation? Defaults to FALSE.

...

further arguments passed to the bootstrap engine when a confidence interval is requested, namely R and type. Any other name is an error rather than a silent no-op.

Value

if conf.level = NA, a numeric scalar. Otherwise a named numeric vector with elements:

est

point estimate of Tukey's biweight mean

lci

lower confidence interval bound

uci

upper confidence interval bound

Details

The biweight mean is a robust location estimator that downweights observations far from the median. It is defined via the tuning constant const (default 9), which controls the breakdown point: larger values are less resistant but more efficient under normality.

When conf.level is not NA a bootstrap confidence interval is returned. The resampling is done in C++; the R random number generator is used only to draw the seed, so set.seed() makes the result reproducible. Bootstrap arguments are passed through ...:

R

Number of bootstrap replicates (default 999).

type

CI type: "perc" or "bca" (default).

The biweight mean is a location estimator and therefore unbounded, so the open side of a one-sided interval is reported at \(\pm\infty\) - unlike the bounded measures in this package, where it is reported at the range limit. See ConfidenceIntervals().

See also

Other location: gmean(), hmean(), hodgesLehmann(), huberM(), meanX(), medianX(), modeX()

Examples

set.seed(1)
x <- c(rnorm(50), 10)   # one outlier

tukeyBiweight(x)
#> [1] 0.1340368

set.seed(2)             # will yield reproducible intervals
tukeyBiweight(x, conf.level = 0.95)
#>        est        lci        uci 
#>  0.1340368 -0.1244454  0.3469211 
tukeyBiweight(x, conf.level = 0.95, type = "perc", R = 499)
#>        est        lci        uci 
#>  0.1340368 -0.0987742  0.3713162 
tukeyBiweight(x, conf.level = 0.95, type = "bca", R = 499)
#>        est        lci        uci 
#>  0.1340368 -0.1150934  0.3618559 

# one-sided: "left" carries the finite lower bound
set.seed(2)
tukeyBiweight(x, conf.level = 0.95, sides = "left")
#>         est         lci         uci 
#>  0.13403675 -0.08950033         Inf