ecdfHT.multivar {ecdfHT}

Multivariate extensions of transformed empirical cdf plot

Description

Transform multivariate data and plot using the ideas from the univariate plot.

Usage

ecdfHT.multivar(x, scale.q = matrix(c(0.25, 0.5, 0.75), nrow = 3, ncol =
  ncol(x)), q0 = 0.5, radii.upper.tail.p = 0.9, p.norm = 2,
  show.axes.labels = FALSE, zscale = c(500, 1), ...)

ecdfHT.multivar.transform(x, scale.q, q0, p.norm)

ecdfHT.2d(multivar.obj, zscale = c(500, 1), ...)

ecdfHT.2d.axes(zscale)

lp.norm(x, p.norm)

Arguments

x

Matrix of data of size (n x d)

scale.q

matrix of sixe (3 x d), probabilities used to determine the scaling and centering for each component

q0

quantile of radii transformation

radii.upper.tail.p

probability used as cutuoff to tail fit; set to 1 to suppress upper tail fit

p.norm

Power used in computing L^p norm

show.axes.labels

Boolean value, determines if axes are labeled or not

zscale

Vector of length 2, value of aspect ratio for the z axis when d=2 and the two 3d plots are drawn

...

Optional graphical parameters, e.g. col='red'

multivar.obj

An object of class 'ecdfHT.multivar', see details.

Details

ecdfHT.multivar gives a quick graphical look at a d dimensional data set. It produces two plots: the first is a superposition of the univariate ecdfHT plots for each component; the second plot is an array of plots, showing one plot for each component.

ecdfHT.bivar produces two plots of a bivariate data set. The first one has three subplots: a scatter plot of the data, a transformed scatterplot of the data, and a univariate ecdfHT plot of the radii of the data. For the second and third subplot, ???? then g(y[,1]) is plotted against g(y[,2]) to get the second plot. For the third plot, compute radius r[i]= l_p norm of shifted and scaled data. These radii are plotted in a univariate, one-sided ecdfHT plot.

The second plot produced is a 3-dimensonal plot. It takes the first two subplots just described and adds a third dimension by looking at an ecdf for the radii. Thus the height of a point is low if the point is near the center, and increases as points move away. The first subplot shows points (x[i,1],x[i,2],ecdf of r[i]). The second plot transforms all three components: it shows (h1(x[i,1]),hs(x[i,2]),g(ecdf of r[i]), where h1(.) and h2(.) are scaled versions of h(.) from the univariate ecdfHT plot, and g(.) is as in the univariate plot. See the vignette for more detail.

Value

ecdfHT.multivar draws several plots, returns a list (invisibly) with fields:

x

input (n x d) matrix of data

x.prime

(n x d) matrix of centered and shifted version of x

y

(n x d) matrix of transformed x

p.norm

what p-norm to use; p.norm=2 is Euclidean norm

scale.q

copy of input argument

radii

vector of length n, p-norm of the rows of x.prime

q0

copy of input value

r0

q0-th quantile of the radii

univariate.ecdfHT

list of length d, with j-th entry the object returned by ecdfHT for the j-th column of x

radii.ecdfHT

list returned from ecdfHT( radii, ... )

radii.tail.fit

object returned from ecdfHT.fit for the radii )

rgl.id

rgl id of 3d plot(s); can be used to access, change, print 3d plots

radii.prob

if d=2, this vector gives the empirical cdf of the radii

radii.prob2

if d=2, this vector gives the transformed empirical cdf of the radii

ecdfHT.multivar.transform computes the transformed vectors y, radii, and lp.norm computes the lp-norm of the rows of x

Examples

# independent components
set.seed(2)
x <- matrix( rcauchy(4000), ncol=4 )
ecdfHT.multivar( x )

# radially symmetric
r <- rcauchy(1000)
theta <- runif(1000,min=0,max=2*pi)
x <- cbind( r*cos(theta), r*sin(theta) )
ecdfHT.multivar( x )