Depth versus depth plot

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Description

Produces a DD plot which allows to compare two multivirate datasets or to compare a subject dataset with theoretical distribution.

Usage

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ddPlot(x, y, scale = FALSE, location = FALSE, name_x = "X",
  name_y = "Y", title = "Depth vs. depth plot", ...)

Arguments

x

The first or only data sample for ddPlot.

y

The second data sample. x and y must be of the same space.

scale

logical. determines whether the dispersion is to be aligned.

location

determines whether the location is to be aligned to 0 vector with depth median.

name_x

name for data set x. It will be passed to drawing function.

name_y

name for data set y.

title

title of the plot.

...

Parameters passed to depth function

Details

For two probability distributions F and G , both in {{{R}}^{d}} , we can define depth vs. depth plot being very useful generalization of the one dimensional quantile-quantile plot:

DD(F,G)=≤ft\{ ≤ft( D({z},F),D({z},G) \right),{z}\in {{{R}}^{d}} \right\}

Its sample counterpart calculated for two samples {{{X}}^{n}}=\{{{X}_{1}},.,{{X}_{n}}\} from F , and {{Y}^{m}}=\{{{Y}_{1}},...,{{Y}_{m}}\} from G is defined as

DD({{F}_{n}},{{G}_{m}})=≤ft\{ ≤ft( D({z},{{F}_{n}}),D({z},{{G}_{m}}) \right),{z}\in \{{{{X}}^{n}}\cup {{{Y}}^{m}}\} \right\}

Author(s)

Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.

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, 822–831.

Liu, R.Y., Singh K. (1993), A Quality Index Based on Data Depth and Multivariate Rank Test, Journal of the American Statistical Association vol. 88.

Examples

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require(sn)
require(mvtnorm)

# EXAMPLE 1: Location difference
standard = mvrnorm(1000, c(0,0), diag(2))
shift    =  mvrnorm(1000, c(0.5, 0), diag(2))
ddPlot(x = standard, y = shift, title = "Difference in position")
ddPlot(x = standard, y = shift, location = TRUE, title = "Location aligned")

## EXAMPLE 2: Scale difference
standard <- mvrnorm(1000, c(0,0), diag(2))
scale <- mvrnorm(1000, c(0,0), 4*diag(2))
ddPlot(x=standard, y=scale)
ddPlot(x=standard, y=scale, scale=TRUE)

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