A location estimator based on the shorth
A location estimator based on the shorth
shorth(x, na.rm=FALSE, tie.action="mean", tie.limit=0.05)
x |
Numeric |
na.rm |
Logical. If |
tie.action |
Character scalar. See details. |
tie.limit |
Numeric scalar. See details. |
The shorth is the shortest interval that covers half of the
values in x. This function calculates the mean of the x
values that lie in the shorth. This was proposed by Andrews (1972) as a
robust estimator of location.
Ties: if there are multiple shortest intervals,
the action specified in ties.action is applied.
Allowed values are mean (the default), max and min.
For mean, the average value is considered; however, an error is
generated if the start indices of the different shortest intervals
differ by more than the fraction tie.limit of length(x).
For min and max, the left-most or right-most, respectively, of
the multiple shortest intervals is considered.
Rate of convergence: as an estimator of location of a unimodal distribution, under regularity conditions, the quantity computed here has an asymptotic rate of only n^{-1/3} and a complicated limiting distribution.
See half.range.mode for an iterative version
that refines the estimate iteratively and has a builtin bootstrapping option.
The mean of the x values that lie in the shorth.
Wolfgang Huber http://www.ebi.ac.uk/huber, Ligia Pedroso Bras
G Sawitzki, “The Shorth Plot.” Available at http://lshorth.r-forge.r-project.org/TheShorthPlot.pdf
DF Andrews, “Robust Estimates of Location.” Princeton University Press (1972).
R Grueble, “The Length of the Shorth.” Annals of Statistics 16, 2:619-628 (1988).
DR Bickel and R Fruehwirth, “On a fast, robust estimator of the mode: Comparisons to other robust estimators with applications.” Computational Statistics & Data Analysis 50, 3500-3530 (2006).
x = c(rnorm(500), runif(500) * 10)
methods = c("mean", "median", "shorth", "half.range.mode")
ests = sapply(methods, function(m) get(m)(x))
if(interactive()) {
colors = 1:4
hist(x, 40, col="orange")
abline(v=ests, col=colors, lwd=3, lty=1:2)
legend(5, 100, names(ests), col=colors, lwd=3, lty=1:2)
}Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.