ordermfrontier.2d {frontiles}

Representation of m-order efficiency frontier for 1 output and 1 input

Description

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

Usage

ordermfrontier.2d(xobs, yobs, type = "output", m = 30, 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"

m

an integer

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 m-order 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.

Examples

# 1st example
data(spain)
plot(y ~ x2, data = spain)
ordermfrontier.2d(as.matrix(spain$x2), as.matrix(spain$y), type = "output",
  m = 30, col = 'red', lty = 2, add = TRUE)
ordermfrontier.2d(as.matrix(spain$x2), as.matrix(spain$y), type = "input", m = 30,
  col = 'royalblue', lty = 3, add = TRUE)
ordermfrontier.2d(as.matrix(spain$x2), as.matrix(spain$y), type = "hyper", m = 30,
  col = 'green', lty = 4, add = TRUE)
legend("topleft", legend = c("output direction", "input direction", "hyper direction"),
  lty = 2:4, col = c("red", "royalblue", "green"))

# 2nd example
ordermfrontier.2d(as.matrix(spain$x2), as.matrix(spain$y), type = "output",
  confidence = TRUE, shade = TRUE, m = 30)