# mediancenter: Mediancenter In fastmatrix: Fast Computation of some Matrices Useful in Statistics

## Description

It calculates the mediancenter (or geometric median) of multivariate data.

## Usage

 `1` ```mediancenter(x) ```

## Arguments

 `x` a matrix or data frame. As usual, rows are observations and columns are variables.

## Details

The mediancenter for a sample of multivariate observations is computed using a steepest descend method combined with bisection. The mediancenter invariant to rotations of axes and is useful as a multivariate generalization of the median of univariate sample.

## Value

A list containing the following named components:

 `median` an estimate for the mediancenter of the data. `iter` the number of iterations performed, it is negative if a degenerate solution is found.

## References

Gower, J.C. (1974). Algorithm AS 78: The mediancentre. Applied Statistics 23, 466-470.

`cov.wt`, `median`.
 ```1 2 3 4 5 6``` ```x <- cbind(1:10, c(1:3, 8:5, 8:10)) z <- mediancenter(x)\$median # degenerate solution xbar <- colMeans(x) plot(x, xlab = "", ylab = "") points(x = xbar[1], y = xbar[2], pch = 16, col = "red") points(x = z[1], y = z[2], pch = 3, col = "blue", lwd = 2) ```