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Last data update: 2014.03.03

R: Representation of alpha-quantile efficiency frontier for 1...

alphafrontier.2d

R Documentation

Representation of alpha-quantile efficiency frontier for 1 output and 1 input

Description

Representation of the alpha-quantile efficiency frontier (output, input or hyperbolic direction) for a set of reference points (xobs, yobs) in 2D (1 output and 1 input).

Usage

alphafrontier.2d(xobs, yobs, type="output", alpha=0.95, add=FALSE, 
confidence=FALSE, shade=FALSE,...)

Arguments

`xobs`	a matrix of size n1 x 1, input of sample points
`yobs`	a matrix of size n1 x 1, output of sample points
`type`	a direction to choose among "output", "input" and "hyper"
`alpha`	a scalar between 0 and 1
`add`	a boolean with TRUE for keeping the active device
`confidence`	a boolean for representing a confidence interval
`shade`	a boolean for shading the confidence interval
`...`	usual options for ploting the frontier, lty, col, etc.

Details

Actually, there is no confidence interval when type="hyper". If type="input" and confidence=TRUE, the y-axis is permuted with the x-axis

Author(s)

Abdelaati Daouia and Thibault Laurent

References

Daouia, A. and L. Simar (2007), Nonparametric efficiency analysis: A multivariate conditional quantile approach, Journal of Econometrics 140, 375-400.

Examples

# 1st example
data(spain)
plot(y~x2,data=spain)
alphafrontier.2d(as.matrix(spain$x2),as.matrix(spain$y),type="output",
alpha=0.95,col='red',lty=2,add=TRUE)
alphafrontier.2d(as.matrix(spain$x2),as.matrix(spain$y),type="input",
alpha=0.95,col='royalblue',lty=3,add=TRUE)
alphafrontier.2d(as.matrix(spain$x2),as.matrix(spain$y),type="hyper",
alpha=0.95,col='green',lty=4,add=TRUE)
legend("topleft",title="alpha-quantile frontier; alpha=0.95",
legend=c("output direction","input direction","hyper direction"),lty=2:4,
col=c("red","royalblue","green"))

# 2nd example
plot(y~x2,data=spain)
alphafrontier.2d(as.matrix(spain$x2),as.matrix(spain$y),
type="output",alpha=1,add=TRUE)
alphafrontier.2d(as.matrix(spain$x2),as.matrix(spain$y),type="output",
alpha=0.95,col='blue',lty=2,add=TRUE)
ordermfrontier.2d(as.matrix(spain$x2),as.matrix(spain$y),type="output",
m=30,col='green',lty=3,add=TRUE)
legend("topleft",title="output direction", legend=c("FDH","alpha=0.95","m=30"),
lty=1:3,col=c("black","royalblue","green"))

# 3rd example
alphafrontier.2d(as.matrix(spain$x2),as.matrix(spain$y),type="output",
confidence=TRUE,shade=TRUE,alpha=0.98)
title("Alpha-quantile frontier with alpha=0.98 and its confidence interval")