A location estimator based on the shorth

Description

A location estimator based on the shorth

Usage

shorth(x, na.rm=FALSE, tie.action="mean", tie.limit=0.05)

Arguments

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.

Value

The mean of the x values that lie in the shorth.

Author(s)

Wolfgang Huber http://www.ebi.ac.uk/huber, Ligia Pedroso Bras

References

• 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).

See Also

half.range.mode

Examples

 
  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) 
  }

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
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Type 'q()' to quit R.

> library(genefilter)
> png(filename="/home/ddbj/snapshot/RGM3/R_BC/result/genefilter/shorth.Rd_%03d_medium.png", width=480, height=480)
> ### Name: shorth
> ### Title: A location estimator based on the shorth
> ### Aliases: shorth
> ### Keywords: arith
> 
> ### ** Examples
> 
>  
>   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) 
> #  }
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>