# depth.mdata

##### Provides the depth measure for multivariate data

Compute measure of centrality of the multivariate data. Type of depth function: simplicial depth (SD), Mahalanobis depth (MhD), Random Half--Space depth (HS), random projection depth (RP) and Likelihood Depth (LD).

- Keywords
- Descriptive

##### Usage

`mdepth.LD(x, xx = x, metric = metric.dist, h = NULL, scale = FALSE, ...)`mdepth.HS(x, xx = x, proj = 50, scale = FALSE, xeps = 1e-15, random = FALSE)

mdepth.RP(x, xx = x, proj = 50, scale = FALSE)

mdepth.MhD(x, xx = x, scale = FALSE)

mdepth.KFSD(x, xx = x, trim = 0.25, h = NULL, scale = FALSE, draw = FALSE)

mdepth.FSD(x, xx = x, trim = 0.25, scale = FALSE, draw = FALSE)

mdepth.FM(x, xx = x, scale = FALSE, dfunc = "TD1")

mdepth.TD(x, xx = x, xeps = 1e-15, scale = FALSE)

mdepth.SD(x, xx = NULL, scale = FALSE)

##### Arguments

- x
is a set of points, a d-column matrix.

- xx
is a d-dimension multivariate reference sample (a d-column matrix) where

`x`

points are evaluated.- metric
Metric function, by default

`metric.dist`

. Distance matrix between`x`

and`xx`

is computed.- h
Bandwidth,

`h>0`

. Default argument values are provided as the 15%--quantile of the distance between`x`

and`xx`

.- scale
=TRUE, scale the depth, see scale.

- …
Further arguments passed to or from other methods.

- proj
are the directions for random projections, by default 500 random projections generated from a scaled

`runif(500,-1,1)`

.- xeps
Accuracy. The left limit of the empirical distribution function.

- random
=TRUE for random projections. =FALSE for deterministic projections.

- trim
The alpha of the trimming.

- draw
=TRUE, draw the curves, the sample median and trimmed mean.

- dfunc
type of univariate depth function used inside depth function: "FM1" refers to the original Fraiman and Muniz univariate depth (default), "TD1" Tukey (Halfspace),"Liu1" for simplical depth, "LD1" for Likelihood depth and "MhD1" for Mahalanobis 1D depth. Also, any user function fulfilling the following pattern

`FUN.USER(x,xx,...)`

and returning a`dep`

component can be included.

##### Details

Type of depth measures:

The

`mdepth.SD`

calculates the simplicial depth (HD) of the points in`x`

w.r.t.`xx`

(for bivariate data).The

`mdepth.HS`

function calculates the random half--space depth (HS) of the points in`x`

w.r.t.`xx`

based on random projections`proj`

.The

`mdepth.MhD`

function calculates the Mahalanobis depth (MhD) of the points in`x`

w.r.t.`xx`

.The

`mdepth.RP`

calculates the random' projection depth (RP) of the points in`x`

w.r.t.`xx`

based on random projections`proj`

.The

`mdepth.LD`

calculates the Likelihood depth (LD) of the points in`x`

w.r.t.`xx`

.The

`mdepth.TD`

function provides the Tukey depth measure for multivariate data.

##### Value

lmed Index of deepest element

`median`

of`xx`

.ltrim Index of set of points

`x`

with trimmed mean`mtrim`

.dep Depth of each point

`x`

w.r.t.`xx`

.proj The projection value of each point on set of points.

xis a set of points to be evaluated.

xx a reference sample

name Name of depth method

##### References

Liu, R. Y., Parelius, J. M., and Singh, K. (1999). Multivariate
analysis by data depth: descriptive statistics, graphics and inference,(with
discussion and a rejoinder by Liu and Singh). *The Annals of
Statistics*, 27(3), 783-858.

##### See Also

Functional depth functions: `depth.FM`

,
`depth.mode`

, `depth.RP`

, `depth.RPD`

and `depth.RT`

.

##### Examples

```
# NOT RUN {
data(iris)
group<-iris[,5]
x<-iris[,1:2]
MhD<-mdepth.MhD(x)
PD<-mdepth.RP(x)
HD<-mdepth.HS(x)
SD<-mdepth.SD(x)
x.setosa<-x[group=="setosa",]
x.versicolor<-x[group=="versicolor",]
x.virginica<-x[group=="virginica",]
d1<-mdepth.SD(x,x.setosa)$dep
d2<-mdepth.SD(x,x.versicolor)$dep
d3<-mdepth.SD(x,x.virginica)$dep
# }
```

*Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2*