depth.spatial {ddalpha} | R Documentation

## Calculate Spatial Depth

### Description

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

### Usage

    depth.spatial(x, data, mah.estimate = "moment", mah.parMcd = 0.75)

### 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.

`mah.estimate`

is a character string specifying which estimates to use when calculating sample covariance matrix; can be `"none"`, `"moment"` or `"MCD"`, determining whether traditional moment or Minimum Covariance Determinant (MCD) (see `covMcd`) estimates for mean and covariance are used. By default `"moment"` is used. With `"none"` the non-affine invariant version of Spatial depth is calculated

`mah.parMcd` | is the value of the argument `alpha` for the function `covMcd`; is used when `mah.estimate =` `"MCD"`.

### Details

Calculates spatial depth. Spatial depth (also L1-depth) is a distance-based depth exploiting the idea of spatial quantiles of Chaudhuri (1996) and Koltchinskii (1997), formulated by Vardi & Zhang (2000) and Serfling (2002).

### Value

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

### References

Chaudhuri, P. (1996). On a geometric notion of quantiles for multivariate data. Journal of the Americal Statistical Association 91 862–872.

Koltchinskii, V.I. (1997). M-estimation, convexity and quantiles. The Annals of Statistics 25 435–477.

Serfling, R. (2006). Depth functions in nonparametric multivariate inference. In: Liu, R., Serfling, R., Souvaine, D. (eds.), Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications, American Mathematical Society, 1–16.

Vardi, Y. and Zhang, C.H. (2000). The multivariate L1-median and associated data depth. Proceedings of the National Academy of Sciences, U.S.A. 97 1423–1426.

### See Also

`depth.halfspace` for calculation of the Tukey depth.

`depth.Mahalanobis` for calculation of Mahalanobis depth.

`depth.projection` for calculation of projection depth.

`depth.simplicial` for calculation of simplicial depth.

`depth.simplicialVolume` for calculation of simplicial volume depth.

`depth.zonoid` for calculation of zonoid depth.

`depth.potential` for calculation of data potential.

### 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.spatial(x, data)
    cat("Depths: ", depths, "\n")

[Package ddalpha version 1.3.9 Index]