# A location estimator based on the shorth

### Description

A location estimator based on the shorth

### Usage

1 |

### Arguments

`x` |
Numeric |

`na.rm` |
Logical. If |

`tie.action` |
Character scalar. See details. |

`tie.limit` |
Numeric scalar. See details. |

### 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

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