alphafrontier.3d {frontiles}

3d representation of alpha-quantile frontier in the case of 2 input and 1 output.

Description

3d representation of alpha-quantile frontier for a set of reference points (xobs,yobs) in the case of two input and one output. No representation yet for hyperbolic direction.

Usage

alphafrontier.3d(xobs, yobs, type="output",alpha=0.95, digits=4, 
box.leg=TRUE, palette=heat_hcl, rgl=FALSE, n.class=NULL,  ...)

Arguments

xobs

a matrix of size n_1 \times 2, input of reference points

yobs

a matrix of size n_1 \times 1, output of reference points

type

a character, "output" or "input" direction

alpha

a scalar

digits

a precision parameter to compute the alpha-frontier

box.leg

representation of a legend-box on the plot with the values of frontier

palette

function to use for colors in case where option col has not been called. See package colorspace for more informations.

rgl

a boolean, for output direction, representation of the graphic in 3d if TRUE

n.class

a numeric, for output direction, the number of class

...

usual parameters of function plot. Use the parameter asp to modify the scale of window...

Details

In "input" direction: You choose a value of output in the legend box, the efficiency-frontier of the input is represented with the corresponding color on the 2d graphic. In "output" direction : For calculate the alpha-quantile efficiency output frontier everywhere, we have constructed a grid of size n \times n by drawing vertical and horizontal lines which intersect each reference observations. Then, we have calculated for each cell C_k k=1,...,n^2 the prediction of the alpha-quantile output efficiency frontier which correspond to the \alpha^{th} elements of the suite \{y_j\}_{j=1,...,n_k} where reference observations j, j=1,...,n_k verify

\ x^1_j\leq\inf_{(x^1,x^2) \in C_k}x^1

and x^2\leq\inf_{(x_1,x_2) \in C_k}x^2.
We propose to use an algorithm which filled up cells with colors depending on the values taken by the alpha-quantile output efficiency frontier. The algorithm attach the row and vary the column as the folling figure can show it.

Value

no values

Note

The algorithm used is certainly not optimized. For a data set of 61 observations, the function necessits 15.17s on an Optiplex GX745 2 duo 2.13GHz under Windows Vista and probably bugs beyond a certain number of observation

Author(s)

Abdelaati Daouia and Thibault Laurent

See Also

alphascore

Examples

data(spain)
xyn <- cbind(spain[, 3:4],spain[, 1])
xtab <- as.matrix(xyn[, c(1,2)])
ytab <- matrix(xyn[, 3])

# representation in 2-d

op <- par(no.readonly = TRUE) # the whole list of settable par's.
alphafrontier.3d(xtab, ytab, type = "output", alpha = 0.6, xlab = "input 1",
 ylab = "input 2", main = "blabla") 
points(xtab, pch = 16)
par(op)