trafoEst: Function trafoEst in Package `distrMod'

Description

trafoEst takes a $τ$ like function (compare trafo-methods) and transforms an existing estimator by means of this transformation.

Usage

trafoEst(fct, estimator)

Value

exactly the argument estimator, but with modified slots

estimate, asvar, and trafo.

Arguments

fct: a $τ$ like function, i.e., a function in the main part $θ$ of the parameter returning a list list(fval, mat) where fval is the function value $τ (θ)$ of the transformation, and mat, its derivative matrix at $θ$ .
estimator: an object of class Estimator.

Details

The disadvantage of this proceeding is that the transformation is not accounted for in determining the estimate (e.g. in a corresponding optimality); it simply transforms an existing estimator, without reapplying it to data. This becomes important in optimally robust estimation.

Examples

Run this code

## Gaussian location and scale
NS <- NormLocationScaleFamily(mean=2, sd=3)
## generate data out of this situation
x <- r(distribution(NS))(30)

## want to estimate mu/sigma, sigma^2
## -> without new trafo slot:
mtrafo <- function(param){
  mu <- param["mean"]
  sd <- param["sd"]
  fval <- c(mu/sd, sd^2)
  nfval <- c("mu/sig", "sig^2")
  names(fval) <- nfval
  mat <- matrix(c(1/sd,0,-mu/sd^2,2*sd),2,2)
  dimnames(mat) <- list(nfval,c("mean","sd"))
  return(list(fval=fval, mat=mat))
}

## Maximum likelihood estimator in the original problem
res0 <- MLEstimator(x = x, ParamFamily = NS)
## transformation
res <- trafoEst(mtrafo, res0)
## confidence interval
 confint(res)