depth.zonoid: Calculate Zonoid Depth
In ddalpha: Depth-Based Classification and Calculation of Data Depth

depth.zonoid

R Documentation

Calculate Zonoid Depth

Description

Calculates the zonoid depth of points w.r.t. a multivariate data set.

Usage

depth.zonoid(x, data, seed = 0)

Arguments

`x`	Matrix of objects (numerical vector as one object) whose depth is to be calculated; each row contains a `d`-variate point. Should have the same dimension as `data`.
`data`	Matrix of data where each row contains a `d`-variate point, w.r.t. which the depth is to be calculated.
`seed`	the random seed. The default value `seed=0` makes no changes.

Details

Calculates zonoid depth (Koshevoy and Mosler, 1997; Mosler, 2002) exactly based on the algorithm of Dyckerhoff, Koshevoy and Mosler (1996), implemented in C++ (and provided) by Rainer Dyckerhoff.

Value

Numerical vector of depths, one for each row in x; or one depth value if x is a numerical vector.

References

Dyckerhoff, R., Koshevoy, G., and Mosler, K. (1996). Zonoid data depth: theory and computation. In: Prat A. (ed), COMPSTAT 1996. Proceedings in computational statistics, Physica-Verlag (Heidelberg), 235–240.

Koshevoy, G. and Mosler, K. (1997). Zonoid trimming for multivariate distributions Annals of Statistics 25 1998–2017.

Mosler, K. (2002). Multivariate dispersion, central regions and depth: the lift zonoid approach Springer (New York).

Examples

# 5-dimensional normal distribution
data <- mvrnorm(1000, rep(0, 5), 
                matrix(c(1, 0, 0, 0, 0, 
                         0, 2, 0, 0, 0, 
                         0, 0, 3, 0, 0, 
                         0, 0, 0, 2, 0, 
                         0, 0, 0, 0, 1),
                nrow = 5))
x <- mvrnorm(10, rep(1, 5), 
             matrix(c(1, 0, 0, 0, 0, 
                      0, 1, 0, 0, 0, 
                      0, 0, 1, 0, 0, 
                      0, 0, 0, 1, 0, 
                      0, 0, 0, 0, 1),
             nrow = 5))
                
depths <- depth.zonoid(x, data)
cat("Depths: ", depths, "\n")

ddalpha documentation built on Oct. 1, 2024, 1:07 a.m.