R: Mahalanobis distances from center of indexed points

mahalanofix {fpc} | R Documentation

## Mahalanobis distances from center of indexed points

### Description

Computes the vector of (classical or robust) Mahalanobis distances of all points of `x` to the center of the points indexed (or weighted) by `gv`. The latter also determine the covariance matrix.

Thought for use within `fixmahal`.

### Usage

    mahalanofix(x, n = nrow(as.matrix(x)), p = ncol(as.matrix(x)), gv =
    rep(1, times = n), cmax = 1e+10, method = "ml")

    mahalanofuz(x, n = nrow(as.matrix(x)), p = ncol(as.matrix(x)),
                             gv = rep(1, times=n), cmax = 1e+10)

### Arguments

`x` | a numerical data matrix, rows are points, columns are variables.
`n` | positive integer. Number of points.
`p` | positive integer. Number of variables.
`gv` | for `mahalanofix` a logical or 0-1 vector of length `n`. For `mahalanofuz` a numerical vector with values between 0 and 1.
`cmax` | positive number. used in `solvecov` if covariance matrix is singular.
`method` | `"ml"`, `"classical"`, `"mcd"` or `"mve"`. Method to compute the covariance matrix estimator. See `cov.rob`, `fixmahal`.

### Details

`solvecov` is used to invert the covariance matrix. The methods `"mcd"` and `"mve"` in `mahalanofix` do not work properly with point constellations with singular covariance matrices!

### Value

A list of the following components:

`md` | vector of Mahalanobis distances.
`mg` | mean of the points indexed by `gv`, weighted mean in `mahalanofuz`.
`covg` | covariance matrix of the points indexed by `gv`, weighted covariance matrix in `mahalanofuz`.
`covinv` | `covg` inverted by `solvecov`.
`coll` | logical. If `TRUE`, `covg` has been (numerically) singular.

### Note

Methods `"mcd"` and `"mve"` require library `lqs`.

### Author(s)

Christian Hennig c.hennig@ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche/

### See Also

`fixmahal`, `solvecov`, `cov.rob`

### Examples

      x <- c(1,2,3,4,5,6,7,8,9,10)
      y <- c(1,2,3,8,7,6,5,8,9,10)
      mahalanofix(cbind(x,y),gv=c(0,0,0,1,1,1,1,1,0,0))
      mahalanofix(cbind(x,y),gv=c(0,0,0,1,1,1,1,0,0,0))
      mahalanofix(cbind(x,y),gv=c(0,0,0,1,1,1,1,1,0,0),method="mcd")
      mahalanofuz(cbind(x,y),gv=c(0,0,0.5,0.5,1,1,1,0.5,0.5,0))

[Package fpc version 2.1-10 Index]