frontiles (version 1.3.1)

ROCscore: The ROC curve to help choosing alpha and m parameters

Description

Computes the percentage of firms super-efficient according to the parameter alpha for alpha-quantile score and m for m-order score in a given direction.

Usage

ROCscore(xobs, yobs, type="output")

Value

a data.frame object with:

alpha

different values of alpha

f(alpha)

the percentage of firms super-efficient

m

different values of m

f(m)

the percentage of firms super-efficient

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

type

a direction to choose among "output", "input" and "hyper"

Author

Abdelaati Daouia and Thibault Laurent

Details

A firm is super-efficient if it score is greater than 1. By consulting this graph, we may choose the values of alpha and m which correspond to the desired degree of robustness, i.e. the percentage of high performers of the population we want to exclude in our more realistic benchmarking comparison (see p.78 of Daraio and Simar, 2010).

References

Daraio and Simar (2007),Advanced Robust and Nonparametric Methods in Efficiency Analysis, Springer.

Examples

# 1st example
data(spain)
res.roc <- ROCscore(xobs = as.matrix(spain[,c(2,3,4)]),
                    yobs = as.matrix(spain[,1]),
                    type = "output")