# Depth functions tools for multivariate analysis

### Description

This is a collection of functions applying depth functions methodology to multivariate analysis. Besides allowing calculation of depth values and depth-based location estimators, the package includes functions for drawing contour plots and perspective plots of depth functions.

### Details

Package: | depth |

Type: | Package |

Version: | 2.0 |

Date: | 2012-08-12 |

License: | GPL-2 |

LazyLoad: | yes |

All functions apply to a multivariate data set. Function `depth`

calculates the depth of a point with respect to the data set. Depth functions covered are Tukey's, Liu's and Oja's. Functions `med`

, `trmean`

and `ctrmean`

return depth-based medians, classical-like trimmed means and centroid trimmed means, respectively. Functions `perspdepth`

and `isodepth`

draw perspective and contour plots, respectively. Functions `sdepth`

, `smed`

, `strmeasure`

and `scontour`

give equivalent results for directional data.

### Author(s)

Maxime Genest <maxime.genest@clevislauzon.qc.ca>, Jean-Claude Masse <jcmasse@mat.ulaval.ca>, Jean-Francois Plante <jfplante@hec.ca>.

Maintainer: Jean-Francois Plante <jfplante@hec.ca>

### References

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), *Ann. Statist.*, **27**, 783–858.

Liu, R.Y. and Singh, K. (1992), Directional data: Concepts of data depth on circles and spheres, *Ann. Statist.*, **20**, 1468–1484.

Mardia, K.V. and Jupp, E.J. (1999). *Directional Statistics*, Wiley.

Small, C.G. (1990), A survey of multidimensional medians, *Int. Statist. Rev.*, **58**, 263–277.

Zuo, Y. amd Serfling, R. (2000), General Notions of Statistical Depth Functions, *Ann. Statist.*, **28**, no. 2, 461–482.

### Examples

1 2 3 4 5 6 7 8 9 | ```
set.seed(159); library(MASS)
mu1 <- c(0,0); mu2 <- c(6,0); sigma <- matrix(c(1,0,0,1), nc = 2)
mixbivnorm <- rbind(mvrnorm(80, mu1, sigma), mvrnorm(20, mu2, sigma))
depth(c(0,0),mixbivnorm)
med(mixbivnorm)
trmean(mixbivnorm, 0.2)
library(rgl)
perspdepth(mixbivnorm, col = "magenta")
isodepth(mixbivnorm, dpth = c(35,5), col = rainbow(2))
``` |