trafo-methods: Methods for function trafo in Package 'distrMod'

In distrMod: Object Oriented Implementation of Probability Models

Methods for function trafo in Package ‘distrMod’

Description

Methods for function trafo in package distrMod; there are accessor (trafo) and replacement (trafo<-) versions.

Usage

trafo(object, param, ...)
## S4 method for signature 'Estimate,missing'
trafo(object,param)
## S4 method for signature 'ParamFamParameter,missing'
trafo(object,param)
## S4 method for signature 'ParamWithScaleAndShapeFamParameter,missing'
trafo(object,param)
## S4 method for signature 'ParamFamily,missing'
trafo(object,param)
## S4 method for signature 'ParamFamily,ParamFamParameter'
trafo(object,param)
## S4 method for signature 'Estimate,ParamFamParameter'
trafo(object,param)
trafo.fct(object)
trafo(object) <- value

Arguments

object	an object of either class Estimate, ParamFamParameter, ParamFamily
param	an object of class ParamFamParameter; the parameter value at which to evaluate the transformation
value	a matrix or a function; if it is a matrix, dimensions must be consistent to the parametric setting; if it is function, it should take one argument param of class ParamFamParameter and return a list of length two with named components fval (the function value, see below) and mat (a matrix — with the same dimensions consistency conditions as above).
...	additional argument(s) for methods; not used so far.

Details

trafo is a slot of class ParamFamParameter, which in turn is a slot of class ParamFamily. It also sort of arises in class Estimate, i.e., all slots can be identified by the information contained in an instance thereof.

As usual, trafo also is the accessor and replacement method for this slot. Its corresponding return value depends on the signature for which the accessor / replacement method is used. More specifically, for trafo, we have methods for the following signatures:

signature Estimate,missing:

returns a list of length two with components fct and mat (see below)

signature Estimate,ParamFamParameter:

returns a list of length two with components fct and mat (see below)

signature ParamFamParameter,missing:

returns a matrix (see below)

signature ParamFamily,missing:

returns a matrix (see below)

signature ParamFamily,ParamFamParameter:

returns a list of length two with components fct and mat (see below)

trafo realizes partial influence curves; i.e.; we are only interested in some possibly lower dimensional smooth (not necessarily linear or even coordinate-wise) aspect/transformation tau of the parameter theta.

For the this function tau(), we provide an accessor trafo.fct for signature ParamFamily-method returning this function.

To be coherent with the corresponding nuisance implementation, we make the following convention:

The full parameter theta is split up coordinate-wise in a main parameter theta' and a nuisance parameter theta'' (which is unknown, too, hence has to be estimated, but only is of secondary interest) and a fixed, known part theta'''.

Without loss of generality, we restrict ourselves to the case that transformation tau only acts on the main parameter theta' — if we want to transform the whole parameter, we only have to assume that both nuisance parameter theta'' and fixed, known part of the parameter theta''' have length 0.

To the implementation:

Slot trafo can either contain a (constant) matrix D_theta or a function

tau: Theta' -> TTheta, theta |-> tau(theta)

mapping main parameter theta' to some range TTheta.

If slot value trafo is a function, besides tau(theta), it will also return the corresponding derivative matrix (d/d theta) (tau(theta)). More specifically, the return value of this function theta is a list with entries fval, the function value tau(theta), and mat, the derivative matrix.

In case trafo is a matrix D, we interpret it as such a derivative matrix (d/d theta) (tau(theta)), and, correspondingly, tau(theta) as the linear mapping tau(theta)=D * theta.

According to the signature, method trafo will return different return value types. For signature

Estimate,missing:

it will return a list with entries fct, the function tau, and mat, the matrix (d/d theta) (tau(theta)). function tau will then return the list list(fval, mat) mentioned above.

Estimate,ParamFamParameter:

as signature Estimate,missing.

ParamFamParameter,missing:

it will just return the corresponding matrix.

ParamFamily,missing:

is just wrapper to signature ParamFamParameter,missing.

ParamFamily,ParamFamParameter:

as signature Estimate,missing.

Examples

## 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
## -> new trafo slot:
trafo(NS) <- 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
(res <- MLEstimator(x = x, ParamFamily = NS))
## confidence interval
 confint(res)

distrMod documentation built on Nov. 16, 2022, 9:07 a.m.