# robLoc: Robust Estimate of Location In revss: Robust Estimation in Very Small Samples

## Description

Compute the robust estimate of location for very small samples.

## Usage

 `1` ```robLoc(x, scale = NULL, na.rm = FALSE, maxit = 80, tol = sqrt(.Machine\$double.eps)) ```

## Arguments

 `x` A numeric vector. `scale` The scale, if known, can be used to enhance the estimate for the location; defaults to unknown. `na.rm` If `TRUE` then `NA` values are stripped from `x` before computation takes place. `maxit` The maximum number of iterations; defaults to 60. `tol` The desired accuracy.

## Details

Computes the M-estimator for location using the logistic ψ function of Rousseeuw & Verboven (2002, 4.1). If there are three or fewer entries, the function defaults to the `median`.

If the scale is known and passed through `scale`, the algorithm uses the suggestion in Rousseeuw & Verboven section 5 (2002), substituting the known scale for the `mad`.

If `na.rm` is `TRUE` then `NA` values are stripped from `x` before computation takes place. If this is not done then an `NA` value in `x` will cause `mad` to return `NA`.

The tolerance and number of iterations are similar to those in existing base R functions.

## Value

Solves for the robust estimate of location, Tn, which is the solution to

mean(ψ((xi - Tn)/Sn)) = 0

where Sn is fixed at `mad(x)`. The ψ-function selected by Rousseeuw & Verboven is:

ψ(x) = (exp(x) - 1) / (exp(x) + 1)

This is equivalent to `2 * plogis(x) - 1`.

## References

Rousseeuw, Peter J. and Verboven, Sabine (2002) Robust estimation in very small samples. Computational Statistics & Data Analysis, 40, (4), 741–758. doi: 10.1016/S0167-9473(02)00078-6

`median`
 ```1 2 3``` ```robLoc(c(1:9)) x <- c(1,2,3,5,7,8) robLoc(x) ```