stoned {Benchmarking} R Documentation

## Convex nonparametric least squares

### Description

Convex nonparametric least squares here for convex (Cost) function function or concave (Production) function with multiplicative or additive error term. the StoNED estimator combines the axiomatic and non-parametric frontier (the DEA aspect) with a stochastic noise term (the SFA aspect)

### Usage

```stoned(X, Y, RTS = "vrs", COST = 0, MULT = 0, METHOD = "MM")
```

### Arguments

 `X` Inputs (right hand side) of firms to be evaluated, a K x m matrix of observations of K firms with m inputs (firm x input). `Y` Output or cost (left hand side) of firms to be evaluated, a K x 1 matrix of observations of K firms with 1 output or cost (firm x input). `RTS` RTS determines returns to scale assumption: RTS="vrs", "drs", "crs" and "irs" are possible for constant or variable returns to scale; see `dea` for a verbal description and numberring scheme. `COST` COST specifies whether a cost function needs is estimated (COST=1) or a production function (COST=0). `MULT` MULT determines if multiplicative (MULT=1) or additive (MULT=0) model is estimated. `METHOD` METHOD specifies the way efficiency is estimated: MM for Method of Momente and PSL for pseudo likelihood estimation.

### Details

Convex nonparametric least squares here for convex (cost) function with multiplicative error term: Y=b*X*exp(e) or additive error term: Y=b*X + e.

### Value

The results are returned in a list with the components:

 `residualNorm` Norm of residual `solutionNorm` Norm of solution `error` Is there an error in the solution?
 `coef` beta_matrix, estimated coefficients as a Kxm matrix; if there is an intercept the first collumn is the intercept, and the matrix is Kx(1+m) `residuals` Residuals `fit` Fitted values `eff` Efficinecy score `front` Points on the frontier `sigma_u` sigma_u

### Note

Convex nonparametric least squares here for convex (Cost) function with multiplicative error term: `Y=b*X*exp(e)` or additive error term: `Y=b*X + e`.

The intercept is absent for the constant returns to scale assumption; all other technology assumptions do have an in tercept.

Note that the method `stoned` is a rather slow method and probably only works in a reasonable time for less than 3-400 units.

### Author(s)

Stefan Seifert s.seifert@ilr.uni-bonn.de and Lars Otto larsot23@gmail.com

### References

Kuosmanen and Kortelainen, "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints", Journal of Productivity Analysis 2012

### Examples

```#### Example: Single Input Production Function
n=10

x1 <- runif(n,10,20)
v <- rnorm(n,0,0.01)
u <- abs(rnorm(n,0,0.04))

y <- (x1^0.8)*exp(-u)*exp(v)

sol_MM <- stoned(x1, y)
sol_PSL <- stoned(x1, y, METHOD="PSL")

plot(x1,y)