frontiles (version 1.3.1)

alphascore: Calculates alpha-quantile efficiency score

Description

Calculates alpha-quantile efficiency score (output, input and hyperbolic direction) for a set of evaluation points (xeval, yeval) depending on reference points (xobs, yobs).

Usage

alphascore(xobs, yobs, xeval=xobs, yeval=yobs, alpha=0.95)

Value

a data.frame object with the alpha-quantile efficiency score in:

output

output direction

input

input direction

hyper

hyperbolic direction

Arguments

xobs

a matrix of size \(n_1 \times p\), input of sample points

yobs

a matrix of size \(n_1 \times q\), output of sample points

xeval

a matrix of size \(n_2 \times p\), input of assessment points

yeval

a matrix of size \(n_2 \times q\), output of assessment points

alpha

a scalar

Author

Abdelaati Daouia and Thibault Laurent

Details

A score between 0 and 1 means that DMU is inefficient. If DMU greater than 1, DMU is super-efficient.

References

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

See Also

alphafrontier.2d, ordermscore

Examples

# 1st example
data(spain)
res.alqf <- alphascore(xobs = as.matrix(spain[, c(2, 3, 4)]),
               yobs = as.matrix(spain[, 1]), alpha = 0.8)

# 2nd example
data(burposte)
bur.samp <- burposte[which(burposte$xinput < 50000), ]
ind.samp <- sample(nrow(bur.samp), 500)
xeval <- as.matrix(bur.samp[ind.samp[1:100], 2])
yeval <- as.matrix(bur.samp[ind.samp[1:100], 3])
xobs <- as.matrix(bur.samp[ind.samp[101:500], 2])
yobs <- as.matrix(bur.samp[ind.samp[101:500], 3])

alphafrontier.2d(xobs, yobs, alpha = 0.95)
points(xeval, yeval, pch = 16, col = 'red')
text(xeval, yeval, as.character(1:100), adj = 2, cex = 0.8)
score.new.0.95 <- alphascore(xobs, yobs, xeval, yeval, alpha = 0.95)