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.