| 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)