alphafrontier.2d {frontiles}

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 n_1 \times 1, input of sample points

yobs

a matrix of size n_1 \times 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

Value

No return value, used for plotting the alpha-quantile efficiency frontier for 1 output and 1 input

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.

See Also

ordermfrontier.2d, alphascore

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")