L2ParamFamily {distrMod} | R Documentation |
Generating function for L2ParamFamily-class
Description
Generates an object of class "L2ParamFamily"
.
Usage
L2ParamFamily(name, distribution = Norm(), distrSymm,
main = main(param), nuisance = nuisance(param),
fixed = fixed(param), trafo = trafo(param),
param = ParamFamParameter(name = paste("Parameter of", name),
main = main, nuisance = nuisance,
fixed = fixed, trafo = trafo),
props = character(0),
startPar = NULL, makeOKPar = NULL,
modifyParam = function(theta){ Norm(mean=theta) },
L2deriv.fct = function(param) {force(theta <- param@main)
return(function(x) {x-theta})},
L2derivSymm, L2derivDistr, L2derivDistrSymm,
FisherInfo.fct, FisherInfo = FisherInfo.fct(param),
.returnClsName = NULL, .withMDE = TRUE)
Arguments
name |
character string: name of the family
|
distribution |
object of class "Distribution" :
member of the family
|
distrSymm |
object of class "DistributionSymmetry" :
symmetry of distribution .
|
main |
numeric vector: main parameter
|
nuisance |
numeric vector: nuisance parameter
|
fixed |
numeric vector: fixed part of the parameter
|
trafo |
function in param or matrix: transformation of the parameter
|
param |
object of class "ParamFamParameter" :
parameter of the family
|
startPar |
startPar is a function in the observations x
returning initial information for MCEstimator used
by optimize resp. optim ; i.e; if (total) parameter is of
length 1, startPar returns a search interval, else it returns an initial
parameter value.
|
makeOKPar |
makeOKPar is a function in the (total)
parameter param ; used if optim resp. optimize —
try to use “illegal” parameter values; then makeOKPar makes
a valid parameter value out of the illegal one; if NULL
slot makeOKPar of ParamFamily is used to produce it.
|
modifyParam |
function: mapping from the parameter space
(represented by "param" ) to the distribution space
(represented by "distribution" ).
|
props |
character vector: properties of the family
|
L2deriv.fct |
function: mapping from the parameter space (argument
param of class "ParamFamParameter" ) to a mapping from
observation x to the value of the L2derivative;
L2deriv.fct is used by modifyModel to
move the L2deriv according to a change in the parameter,
and to fill slot L2deriv .
More specifically, let us call the parts main and nuisance
of the parameter the unknown parameter. If this unknown parameter is
one-dimensional, the return value of L2deriv.fct must be a function
in argument x , which is vectorized, (i.e.,
callable for a vector-valued x ), and has a one-dimensional, numeric
return value. In case the dimension of the unknown parameter is larger
than one, the return value must be a list of functions, each of which
satisfies the conditions formulated for the case of a one-dimensional
parameter of interest. The order of the components of this list is
the same as the order of the parameter coordinates in main , followed
by the ones in nuisance .
|
L2derivSymm |
object of class "FunSymmList" :
symmetry of the maps contained in L2deriv ; a list
of symmetry properties of the same length as the return value of
L2deriv.fct .
|
L2derivDistr |
object of class "UnivarDistrList" :
distribution of L2deriv ; the length of this list
of univariate distributions must be of the same length as the
return value of L2deriv.fct .
|
L2derivDistrSymm |
object of class "DistrSymmList" :
symmetry of the distributions contained in L2derivDistr ;
the length of this list of symmetry properties must be
of the same length as the return value of L2deriv.fct .
|
FisherInfo.fct |
function: mapping from the parameter space (argument
param of class "ParamFamParameter" ) to the set of positive
semidefinite matrices; FisherInfo.fct is used by modifyModel to
move the Fisher information according to a change in the parameter
|
FisherInfo |
object of class "PosSemDefSymmMatrix" :
Fisher information of the family
|
.returnClsName |
the class name of the return value; by default this
argument is NULL whereupon the return class will be
L2ParamFamily ; but, internally, this generating function is also
used to e.g. produce objects of class BinomialFamily , PoisFamily
GammaFamily , BetaFamily .
|
.withMDE |
logical of length 1: Tells R how to use the function from
slot startPar in case of a kStepEstimator —use it as is or
to compute the starting point for a minimum distance estimator which in
turn then serves as starting point for roptest / robest
(from package ROptEst). If TRUE (default) the latter
alternative is used. Ignored if ROptEst is not used.
|
Details
If name
is missing, the default
“L2 differentiable parametric family of probability measures”
is used. In case distrSymm
is missing it is set to
NoSymmetry()
.
If param
is missing, the parameter is created via
main
, nuisance
and trafo
as described
in ParamFamParameter
. In case L2derivSymm
is
missing, it is filled with an object of class FunSymmList
with entries NonSymmetric()
. In case L2derivDistr
is missing,
it is computed via imageDistr
. If L2derivDistrSymm
is missing,
it is set to an object of class DistrSymmList
with entries
NoSymmetry()
. In case FisherInfo
is missing, it is computed
from L2deriv
using E
.
Value
Object of class "L2ParamFamily"
Author(s)
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
References
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness.
Bayreuth: Dissertation.
See Also
L2ParamFamily-class
Examples
F1 <- L2ParamFamily()
plot(F1)
[Package
distrMod version 2.8.2
Index]