frontiles (version 1.3.1)

alphafrontier.2d: 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,...)

Value

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

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.

Author

Abdelaati Daouia and Thibault Laurent

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

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")