L2ParamFamily {distrMod} | R Documentation |
Generates an object of class "L2ParamFamily"
.
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)
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 |
L2derivSymm |
object of class "FunSymmList" :
symmetry of the maps contained in L2deriv |
L2derivDistr |
object of class "UnivarDistrList" :
distribution of L2deriv |
L2derivDistrSymm |
object of class "DistrSymmList" :
symmetry of the distributions contained in L2derivDistr |
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 produce objects of class BinomialFamily , PoisFamily
GammaFamily , BetaFamily . |
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
.
Object of class "L2ParamFamily"
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- L2ParamFamily() plot(F1)