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Last data update: 2014.03.03

R: Calculates alpha-quantile efficiency score

alphascore

R Documentation

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)

Arguments

`xobs`	a matrix of size n1 x p, input of sample points
`yobs`	a matrix of size n1 x q, output of sample points
`xeval`	a matrix of size n2 x p, input of assessment points
`yeval`	a matrix of size n2 x q, output of assessment points
`alpha`	a scalar

Details

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

Value

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

`output`	output direction
`input`	input direction
`hyper`	hyperbolic direction

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)
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,text=as.character(1:100),adj=2,cex=0.8)
score.new.0.95<-alphascore(xobs,yobs,xeval,yeval,alpha=0.95)