Methods for function trafo in Package ‘distrMod’
Methods for function trafo in package distrMod;
there are accessor (trafo) and replacement (trafo<-)
versions.
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
object |
an object of either class |
param |
an object of class |
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 |
... |
additional argument(s) for methods; not used so far. |
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.
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.
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.
The return value depends on the signature.
For trafo.fct, we return the corresponding function
tau() (see below).
For trafo, we have:
signature |
a list of length two with components
|
signature |
a list of length two with components
|
signature |
a matrix (see below) |
signature |
a matrix (see below) |
signature |
a list of length two
with components |
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.